x^2+22x+105-240=0

Solution for x^2+22x+105-240=0 equation:

x^2+22x+105-240=0

We add all the numbers together, and all the variables

x^2+22x-135=0

a = 1; b = 22; c = -135;
Δ = b2-4ac
Δ = 222-4·1·(-135)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-32}{2*1}=\frac{-54}{2}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+32}{2*1}=\frac{10}{2}
=5
$