6-2y(y-6)=4y-7

Solution for 6-2y(y-6)=4y-7 equation:

6-2y(y-6)=4y-7

We move all terms to the left:

6-2y(y-6)-(4y-7)=0

We multiply parentheses

-2y^2+12y-(4y-7)+6=0

We get rid of parentheses

-2y^2+12y-4y+7+6=0

We add all the numbers together, and all the variables

-2y^2+8y+13=0

a = -2; b = 8; c = +13;
Δ = b2-4ac
Δ = 82-4·(-2)·13
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{42}}{2*-2}=\frac{-8-2\sqrt{42}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{42}}{2*-2}=\frac{-8+2\sqrt{42}}{-4}
$