0=4x^2-24x-13

Solution for 0=4x^2-24x-13 equation:

0=4x^2-24x-13

We move all terms to the left:

0-(4x^2-24x-13)=0

We add all the numbers together, and all the variables

-(4x^2-24x-13)=0

We get rid of parentheses

-4x^2+24x+13=0

a = -4; b = 24; c = +13;
Δ = b2-4ac
Δ = 242-4·(-4)·13
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-28}{2*-4}=\frac{-52}{-8}
=6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+28}{2*-4}=\frac{4}{-8}
=-1/2
$