-4(y-5)y=6.

Solution for -4(y-5)y=6. equation:

-4(y-5)y=6.

We move all terms to the left:

-4(y-5)y-(6.)=0

We add all the numbers together, and all the variables

-4(y-5)y-6=0

We multiply parentheses

-4y^2+20y-6=0

a = -4; b = 20; c = -6;
Δ = b2-4ac
Δ = 202-4·(-4)·(-6)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{19}}{2*-4}=\frac{-20-4\sqrt{19}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{19}}{2*-4}=\frac{-20+4\sqrt{19}}{-8}
$