X2-45x-90=0

Solution for X2-45x-90=0 equation:

X2-45X-90=0

We add all the numbers together, and all the variables

X^2-45X-90=0

a = 1; b = -45; c = -90;
Δ = b2-4ac
Δ = -452-4·1·(-90)
Δ = 2385
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:

$\sqrt{\Delta}=\sqrt{2385}=\sqrt{9*265}=\sqrt{9}*\sqrt{265}=3\sqrt{265}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{265}}{2*1}=\frac{45-3\sqrt{265}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{265}}{2*1}=\frac{45+3\sqrt{265}}{2}
$