X^2-24x-90=0

Solution for X^2-24x-90=0 equation:

X^2-24X-90=0

a = 1; b = -24; c = -90;
Δ = b2-4ac
Δ = -242-4·1·(-90)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{26}}{2*1}=\frac{24-6\sqrt{26}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{26}}{2*1}=\frac{24+6\sqrt{26}}{2}
$