X^2-10x-22.5*5=0

Solution for X^2-10x-22.5*5=0 equation:

X^2-10X-22.5*5=0

We add all the numbers together, and all the variables

X^2-10X-112.5=0

a = 1; b = -10; c = -112.5;
Δ = b2-4ac
Δ = -102-4·1·(-112.5)
Δ = 550
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:

$\sqrt{\Delta}=\sqrt{550}=\sqrt{25*22}=\sqrt{25}*\sqrt{22}=5\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-5\sqrt{22}}{2*1}=\frac{10-5\sqrt{22}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+5\sqrt{22}}{2*1}=\frac{10+5\sqrt{22}}{2}
$