2x^2+6x=360^2

Solution for 2x^2+6x=360^2 equation:

2x^2+6x=360^2

We move all terms to the left:

2x^2+6x-(360^2)=0

We add all the numbers together, and all the variables

2x^2+6x-129600=0

a = 2; b = 6; c = -129600;
Δ = b2-4ac
Δ = 62-4·2·(-129600)
Δ = 1036836
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:

$\sqrt{\Delta}=\sqrt{1036836}=\sqrt{36*28801}=\sqrt{36}*\sqrt{28801}=6\sqrt{28801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{28801}}{2*2}=\frac{-6-6\sqrt{28801}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{28801}}{2*2}=\frac{-6+6\sqrt{28801}}{4}
$