0=8x^2-13x-4

Solution for 0=8x^2-13x-4 equation:

0=8x^2-13x-4

We move all terms to the left:

0-(8x^2-13x-4)=0

We add all the numbers together, and all the variables

-(8x^2-13x-4)=0

We get rid of parentheses

-8x^2+13x+4=0

a = -8; b = 13; c = +4;
Δ = b2-4ac
Δ = 132-4·(-8)·4
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3\sqrt{33}}{2*-8}=\frac{-13-3\sqrt{33}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3\sqrt{33}}{2*-8}=\frac{-13+3\sqrt{33}}{-16}
$