x2-24x-320=0

Solution for x2-24x-320=0 equation:

x2-24x-320=0

We add all the numbers together, and all the variables

x^2-24x-320=0

a = 1; b = -24; c = -320;
Δ = b2-4ac
Δ = -242-4·1·(-320)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{29}}{2*1}=\frac{24-8\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{29}}{2*1}=\frac{24+8\sqrt{29}}{2}
$