0=8x^2+24x-11

Solution for 0=8x^2+24x-11 equation:

0=8x^2+24x-11

We move all terms to the left:

0-(8x^2+24x-11)=0

We add all the numbers together, and all the variables

-(8x^2+24x-11)=0

We get rid of parentheses

-8x^2-24x+11=0

a = -8; b = -24; c = +11;
Δ = b2-4ac
Δ = -242-4·(-8)·11
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{58}}{2*-8}=\frac{24-4\sqrt{58}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{58}}{2*-8}=\frac{24+4\sqrt{58}}{-16}
$