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 = 20
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:

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