20x^2-3997x=-800

Solution for 20x^2-3997x=-800 equation:

20x^2-3997x=-800

We move all terms to the left:

20x^2-3997x-(-800)=0

We add all the numbers together, and all the variables

20x^2-3997x+800=0

a = 20; b = -3997; c = +800;
Δ = b2-4ac
Δ = -39972-4·20·800
Δ = 15912009
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:

$\sqrt{\Delta}=\sqrt{15912009}=\sqrt{9*1768001}=\sqrt{9}*\sqrt{1768001}=3\sqrt{1768001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3997)-3\sqrt{1768001}}{2*20}=\frac{3997-3\sqrt{1768001}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3997)+3\sqrt{1768001}}{2*20}=\frac{3997+3\sqrt{1768001}}{40}
$