2x^2+3x=560^2

Solution for 2x^2+3x=560^2 equation:

2x^2+3x=560^2

We move all terms to the left:

2x^2+3x-(560^2)=0

We add all the numbers together, and all the variables

2x^2+3x-313600=0

a = 2; b = 3; c = -313600;
Δ = b2-4ac
Δ = 32-4·2·(-313600)
Δ = 2508809
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:

$\sqrt{\Delta}=\sqrt{2508809}=\sqrt{289*8681}=\sqrt{289}*\sqrt{8681}=17\sqrt{8681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-17\sqrt{8681}}{2*2}=\frac{-3-17\sqrt{8681}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17\sqrt{8681}}{2*2}=\frac{-3+17\sqrt{8681}}{4}
$