5x+x^2=575

Solution for 5x+x^2=575 equation:

5x+x^2=575

We move all terms to the left:

5x+x^2-(575)=0

a = 1; b = 5; c = -575;
Δ = b2-4ac
Δ = 52-4·1·(-575)
Δ = 2325
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:

$\sqrt{\Delta}=\sqrt{2325}=\sqrt{25*93}=\sqrt{25}*\sqrt{93}=5\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{93}}{2*1}=\frac{-5-5\sqrt{93}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{93}}{2*1}=\frac{-5+5\sqrt{93}}{2}
$