12y2-y+5=0

Combine 12 and y2.

y22-y+5=0

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 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