0=4x^2+97x+520

Solution for 0=4x^2+97x+520 equation:

0=4x^2+97x+520

We move all terms to the left:

0-(4x^2+97x+520)=0

We add all the numbers together, and all the variables

-(4x^2+97x+520)=0

We get rid of parentheses

-4x^2-97x-520=0

a = -4; b = -97; c = -520;
Δ = b2-4ac
Δ = -972-4·(-4)·(-520)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-97)-33}{2*-4}=\frac{64}{-8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-97)+33}{2*-4}=\frac{130}{-8}
=-16+1/4
$