12(7-y)=8(y-1)y=

Solution for 12(7-y)=8(y-1)y= equation:

12(7-y)=8(y-1)y=

We move all terms to the left:

12(7-y)-(8(y-1)y)=0

We add all the numbers together, and all the variables

12(-1y+7)-(8(y-1)y)=0

We multiply parentheses

-12y-(8(y-1)y)+84=0


We calculate terms in parentheses: -(8(y-1)y), so:

8(y-1)y

We multiply parentheses

8y^2-8y

Back to the equation:

-(8y^2-8y)


We get rid of parentheses

-8y^2-12y+8y+84=0

We add all the numbers together, and all the variables

-8y^2-4y+84=0

a = -8; b = -4; c = +84;
Δ = b2-4ac
Δ = -42-4·(-8)·84
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-52}{2*-8}=\frac{-48}{-16}
=+3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+52}{2*-8}=\frac{56}{-16}
=-3+1/2
$