-4y^2+56y=36

Solution for -4y^2+56y=36 equation:

-4y^2+56y=36

We move all terms to the left:

-4y^2+56y-(36)=0

a = -4; b = 56; c = -36;
Δ = b2-4ac
Δ = 562-4·(-4)·(-36)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16\sqrt{10}}{2*-4}=\frac{-56-16\sqrt{10}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16\sqrt{10}}{2*-4}=\frac{-56+16\sqrt{10}}{-8}
$