2x^2+3x^=117^2

Solution for 2x^2+3x^=117^2 equation:

2x^2+3x^=117^2

We move all terms to the left:

2x^2+3x^-(117^2)=0

We add all the numbers together, and all the variables

2x^2+3x-13689=0

a = 2; b = 3; c = -13689;
Δ = b2-4ac
Δ = 32-4·2·(-13689)
Δ = 109521
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:

$\sqrt{\Delta}=\sqrt{109521}=\sqrt{9*12169}=\sqrt{9}*\sqrt{12169}=3\sqrt{12169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{12169}}{2*2}=\frac{-3-3\sqrt{12169}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{12169}}{2*2}=\frac{-3+3\sqrt{12169}}{4}
$