x^2+2x-3+x^2+3x-8=360

Solution for x^2+2x-3+x^2+3x-8=360 equation:

x^2+2x-3+x^2+3x-8=360

We move all terms to the left:

x^2+2x-3+x^2+3x-8-(360)=0

We add all the numbers together, and all the variables

2x^2+5x-371=0

a = 2; b = 5; c = -371;
Δ = b2-4ac
Δ = 52-4·2·(-371)
Δ = 2993
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{2993}}{2*2}=\frac{-5-\sqrt{2993}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{2993}}{2*2}=\frac{-5+\sqrt{2993}}{4}
$