-7(y-6)y=8

Solution for -7(y-6)y=8 equation:

-7(y-6)y=8

We move all terms to the left:

-7(y-6)y-(8)=0

We multiply parentheses

-7y^2+42y-8=0

a = -7; b = 42; c = -8;
Δ = b2-4ac
Δ = 422-4·(-7)·(-8)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{385}}{2*-7}=\frac{-42-2\sqrt{385}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{385}}{2*-7}=\frac{-42+2\sqrt{385}}{-14}
$