# Solve for y y^2-3y=3/4 y2-3y=34
Move 34 to the left side of the equation by subtracting it from both sides.
y2-3y-34=0
Multiply through by the least common denominator 4, then simplify.
Apply the distributive property.
4y2+4(-3y)+4(-34)=0
Simplify.
Multiply -3 by 4.
4y2-12y+4(-34)=0
Cancel the common factor of 4.
Move the leading negative in -34 into the numerator.
4y2-12y+4(-34)=0
Cancel the common factor.
4y2-12y+4(-34)=0
Rewrite the expression.
4y2-12y-3=0
4y2-12y-3=0
4y2-12y-3=0
4y2-12y-3=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=4, b=-12, and c=-3 into the quadratic formula and solve for y.
12±(-12)2-4⋅(4⋅-3)2⋅4
Simplify.
Simplify the numerator.
Raise -12 to the power of 2.
y=12±144-4⋅(4⋅-3)2⋅4
Multiply 4 by -3.
y=12±144-4⋅-122⋅4
Multiply -4 by -12.
y=12±144+482⋅4
Add 144 and 48.
y=12±1922⋅4
Rewrite 192 as 82⋅3.
Factor 64 out of 192.
y=12±64(3)2⋅4
Rewrite 64 as 82.
y=12±82⋅32⋅4
y=12±82⋅32⋅4
Pull terms out from under the radical.
y=12±832⋅4
y=12±832⋅4
Multiply 2 by 4.
y=12±838
Simplify 12±838.
y=3±232
y=3±232
The final answer is the combination of both solutions.
y=3+232,3-232
The result can be shown in multiple forms.
Exact Form:
y=3+232,3-232
Decimal Form:
y=3.23205080…,-0.23205080…
Solve for y y^2-3y=3/4

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