x^2+x^2-2x-15=165

Solution for x^2+x^2-2x-15=165 equation:

x^2+x^2-2x-15=165

We move all terms to the left:

x^2+x^2-2x-15-(165)=0

We add all the numbers together, and all the variables

2x^2-2x-180=0

a = 2; b = -2; c = -180;
Δ = b2-4ac
Δ = -22-4·2·(-180)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-38}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+38}{2*2}=\frac{40}{4}
=10
$