x^2-23x-370+x+15=180

Solution for x^2-23x-370+x+15=180 equation:

x^2-23x-370+x+15=180

We move all terms to the left:

x^2-23x-370+x+15-(180)=0

We add all the numbers together, and all the variables

x^2-22x-535=0

a = 1; b = -22; c = -535;
Δ = b2-4ac
Δ = -222-4·1·(-535)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8\sqrt{41}}{2*1}=\frac{22-8\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8\sqrt{41}}{2*1}=\frac{22+8\sqrt{41}}{2}
$