# Solve for y 3/6y^2-2/6y+4/6=0 36y2-26y+46=0
Simplify each term.
Cancel the common factor of 3 and 6.
Factor 3 out of 3.
3(1)6y2-26y+46=0
Cancel the common factors.
Factor 3 out of 6.
3⋅13⋅2y2-26y+46=0
Cancel the common factor.
3⋅13⋅2y2-26y+46=0
Rewrite the expression.
12y2-26y+46=0
12y2-26y+46=0
12y2-26y+46=0
Combine 12 and y2.
y22-26y+46=0
Cancel the common factor of 2 and 6.
Factor 2 out of 2.
y22-2(1)6y+46=0
Cancel the common factors.
Factor 2 out of 6.
y22-2⋅12⋅3y+46=0
Cancel the common factor.
y22-2⋅12⋅3y+46=0
Rewrite the expression.
y22-13y+46=0
y22-13y+46=0
y22-13y+46=0
Combine y and 13.
y22-y3+46=0
Cancel the common factor of 4 and 6.
Factor 2 out of 4.
y22-y3+2(2)6=0
Cancel the common factors.
Factor 2 out of 6.
y22-y3+2⋅22⋅3=0
Cancel the common factor.
y22-y3+2⋅22⋅3=0
Rewrite the expression.
y22-y3+23=0
y22-y3+23=0
y22-y3+23=0
y22-y3+23=0
Multiply through by the least common denominator 6, then simplify.
Apply the distributive property.
6(y22)+6(-y3)+6(23)=0
Simplify.
Cancel the common factor of 2.
Factor 2 out of 6.
2(3)(y22)+6(-y3)+6(23)=0
Cancel the common factor.
2⋅(3(y22))+6(-y3)+6(23)=0
Rewrite the expression.
3y2+6(-y3)+6(23)=0
3y2+6(-y3)+6(23)=0
Cancel the common factor of 3.
Move the leading negative in -y3 into the numerator.
3y2+6(-y3)+6(23)=0
Factor 3 out of 6.
3y2+3(2)(-y3)+6(23)=0
Cancel the common factor.
3y2+3⋅(2(-y3))+6(23)=0
Rewrite the expression.
3y2+2(-y)+6(23)=0
3y2+2(-y)+6(23)=0
Multiply -1 by 2.
3y2-2y+6(23)=0
Cancel the common factor of 3.
Factor 3 out of 6.
3y2-2y+3(2)(23)=0
Cancel the common factor.
3y2-2y+3⋅(2(23))=0
Rewrite the expression.
3y2-2y+2⋅2=0
3y2-2y+2⋅2=0
Multiply 2 by 2.
3y2-2y+4=0
3y2-2y+4=0
3y2-2y+4=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=3, b=-2, and c=4 into the quadratic formula and solve for y.
2±(-2)2-4⋅(3⋅4)2⋅3
Simplify.
Simplify the numerator.
Raise -2 to the power of 2.
y=2±4-4⋅(3⋅4)2⋅3
Multiply 3 by 4.
y=2±4-4⋅122⋅3
Multiply -4 by 12.
y=2±4-482⋅3
Subtract 48 from 4.
y=2±-442⋅3
Rewrite -44 as -1(44).
y=2±-1⋅442⋅3
Rewrite -1(44) as -1⋅44.
y=2±-1⋅442⋅3
Rewrite -1 as i.
y=2±i⋅442⋅3
Rewrite 44 as 22⋅11.
Factor 4 out of 44.
y=2±i⋅4(11)2⋅3
Rewrite 4 as 22.
y=2±i⋅22⋅112⋅3
y=2±i⋅22⋅112⋅3
Pull terms out from under the radical.
y=2±i⋅(211)2⋅3
Move 2 to the left of i.
y=2±2i112⋅3
y=2±2i112⋅3
Multiply 2 by 3.
y=2±2i116
Simplify 2±2i116.
y=1±i113
y=1±i113
The final answer is the combination of both solutions.
y=1+i113,1-i113
Solve for y 3/6y^2-2/6y+4/6=0

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