-5x^2+20x=-19

Solution for -5x^2+20x=-19 equation:

-5x^2+20x=-19

We move all terms to the left:

-5x^2+20x-(-19)=0

We add all the numbers together, and all the variables

-5x^2+20x+19=0

a = -5; b = 20; c = +19;
Δ = b2-4ac
Δ = 202-4·(-5)·19
Δ = 780
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{195}}{2*-5}=\frac{-20-2\sqrt{195}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{195}}{2*-5}=\frac{-20+2\sqrt{195}}{-10}
$