(-4y^2)-20y+7=0

Solution for (-4y^2)-20y+7=0 equation:

(-4y^2)-20y+7=0

We get rid of parentheses

-4y^2-20y+7=0

a = -4; b = -20; c = +7;
Δ = b2-4ac
Δ = -202-4·(-4)·7
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16\sqrt{2}}{2*-4}=\frac{20-16\sqrt{2}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16\sqrt{2}}{2*-4}=\frac{20+16\sqrt{2}}{-8}
$