x^2-14x+x^2=240

Solution for x^2-14x+x^2=240 equation:

x^2-14x+x^2=240

We move all terms to the left:

x^2-14x+x^2-(240)=0

We add all the numbers together, and all the variables

2x^2-14x-240=0

a = 2; b = -14; c = -240;
Δ = b2-4ac
Δ = -142-4·2·(-240)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-46}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+46}{2*2}=\frac{60}{4}
=15
$