0=4x^2-59x-131

Solution for 0=4x^2-59x-131 equation:

0=4x^2-59x-131

We move all terms to the left:

0-(4x^2-59x-131)=0

We add all the numbers together, and all the variables

-(4x^2-59x-131)=0

We get rid of parentheses

-4x^2+59x+131=0

a = -4; b = 59; c = +131;
Δ = b2-4ac
Δ = 592-4·(-4)·131
Δ = 5577
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:

$\sqrt{\Delta}=\sqrt{5577}=\sqrt{169*33}=\sqrt{169}*\sqrt{33}=13\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-13\sqrt{33}}{2*-4}=\frac{-59-13\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+13\sqrt{33}}{2*-4}=\frac{-59+13\sqrt{33}}{-8}
$