2531.25=225x+5x^2

Solution for 2531.25=225x+5x^2 equation:

2531.25=225x+5x^2

We move all terms to the left:

2531.25-(225x+5x^2)=0

We get rid of parentheses

-5x^2-225x+2531.25=0

a = -5; b = -225; c = +2531.25;
Δ = b2-4ac
Δ = -2252-4·(-5)·2531.25
Δ = 101250
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:

$\sqrt{\Delta}=\sqrt{101250}=\sqrt{50625*2}=\sqrt{50625}*\sqrt{2}=225\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-225\sqrt{2}}{2*-5}=\frac{225-225\sqrt{2}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+225\sqrt{2}}{2*-5}=\frac{225+225\sqrt{2}}{-10}
$