Solve for y (-4y+3)/2=7/(2y)

Math
-4y+32=72y
Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.
(-4y+3)⋅(2y)=2⋅7
Solve the equation for y.
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Multiply 2 by 7.
(-4y+3)⋅(2y)=14
Divide each term by 2 and simplify.
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Divide each term in (-4y+3)⋅(2y)=14 by 2.
(-4y+3)⋅(2y)2=142
Simplify (-4y+3)⋅(2y)2.
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Cancel the common factor of 2.
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Cancel the common factor.
(-4y+3)⋅(2y)2=142
Divide (-4y+3)⋅(y) by 1.
(-4y+3)⋅(y)=142
(-4y+3)⋅(y)=142
Apply the distributive property.
-4y⋅y+3y=142
Multiply y by y by adding the exponents.
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Move y.
-4(y⋅y)+3y=142
Multiply y by y.
-4y2+3y=142
-4y2+3y=142
-4y2+3y=142
Divide 14 by 2.
-4y2+3y=7
-4y2+3y=7
Move 7 to the left side of the equation by subtracting it from both sides.
-4y2+3y-7=0
Factor -1 out of -4y2+3y-7.
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Factor -1 out of -4y2.
-(4y2)+3y-7=0
Factor -1 out of 3y.
-(4y2)-(-3y)-7=0
Rewrite -7 as -1(7).
-(4y2)-(-3y)-1⋅7=0
Factor -1 out of -(4y2)-(-3y).
-(4y2-3y)-1⋅7=0
Factor -1 out of -(4y2-3y)-1(7).
-(4y2-3y+7)=0
-(4y2-3y+7)=0
Multiply each term in -(4y2-3y+7)=0 by -1
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Multiply each term in -(4y2-3y+7)=0 by -1.
-(4y2-3y+7)⋅-1=0⋅-1
Simplify -(4y2-3y+7)⋅-1.
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Apply the distributive property.
(-(4y2)-(-3y)-1⋅7)⋅-1=0⋅-1
Simplify.
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Multiply 4 by -1.
(-4y2-(-3y)-1⋅7)⋅-1=0⋅-1
Multiply -3 by -1.
(-4y2+3y-1⋅7)⋅-1=0⋅-1
Multiply -1 by 7.
(-4y2+3y-7)⋅-1=0⋅-1
(-4y2+3y-7)⋅-1=0⋅-1
Apply the distributive property.
-4y2⋅-1+3y⋅-1-7⋅-1=0⋅-1
Simplify.
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Multiply -1 by -4.
4y2+3y⋅-1-7⋅-1=0⋅-1
Multiply -1 by 3.
4y2-3y-7⋅-1=0⋅-1
Multiply -7 by -1.
4y2-3y+7=0⋅-1
4y2-3y+7=0⋅-1
4y2-3y+7=0⋅-1
Multiply 0 by -1.
4y2-3y+7=0
4y2-3y+7=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=-3, and c=7 into the quadratic formula and solve for y.
3±(-3)2-4⋅(4⋅7)2⋅4
Simplify.
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Simplify the numerator.
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Raise -3 to the power of 2.
y=3±9-4⋅(4⋅7)2⋅4
Multiply 4 by 7.
y=3±9-4⋅282⋅4
Multiply -4 by 28.
y=3±9-1122⋅4
Subtract 112 from 9.
y=3±-1032⋅4
Rewrite -103 as -1(103).
y=3±-1⋅1032⋅4
Rewrite -1(103) as -1⋅103.
y=3±-1⋅1032⋅4
Rewrite -1 as i.
y=3±i1032⋅4
y=3±i1032⋅4
Multiply 2 by 4.
y=3±i1038
y=3±i1038
The final answer is the combination of both solutions.
y=3+i1038,3-i1038
y=3+i1038,3-i1038
Solve for y (-4y+3)/2=7/(2y)

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