# Solve for y 1/2y^2-y+5=0 12y2-y+5=0
Combine 12 and y2.
y22-y+5=0
Multiply through by the least common denominator 2, then simplify.
Apply the distributive property.
2(y22)+2(-y)+2⋅5=0
Simplify.
Cancel the common factor of 2.
Cancel the common factor.
2(y22)+2(-y)+2⋅5=0
Rewrite the expression.
y2+2(-y)+2⋅5=0
y2+2(-y)+2⋅5=0
Multiply -1 by 2.
y2-2y+2⋅5=0
Multiply 2 by 5.
y2-2y+10=0
y2-2y+10=0
y2-2y+10=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-2, and c=10 into the quadratic formula and solve for y.
2±(-2)2-4⋅(1⋅10)2⋅1
Simplify.
Simplify the numerator.
Raise -2 to the power of 2.
y=2±4-4⋅(1⋅10)2⋅1
Multiply 10 by 1.
y=2±4-4⋅102⋅1
Multiply -4 by 10.
y=2±4-402⋅1
Subtract 40 from 4.
y=2±-362⋅1
Rewrite -36 as -1(36).
y=2±-1⋅362⋅1
Rewrite -1(36) as -1⋅36.
y=2±-1⋅362⋅1
Rewrite -1 as i.
y=2±i⋅362⋅1
Rewrite 36 as 62.
y=2±i⋅622⋅1
Pull terms out from under the radical, assuming positive real numbers.
y=2±i⋅62⋅1
Move 6 to the left of i.
y=2±6i2⋅1
y=2±6i2⋅1
Multiply 2 by 1.
y=2±6i2
Simplify 2±6i2.
y=1±3i
y=1±3i
The final answer is the combination of both solutions.
y=1+3i,1-3i
Solve for y 1/2y^2-y+5=0

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