10x+x^2=231

Solution for 10x+x^2=231 equation:

10x+x^2=231

We move all terms to the left:

10x+x^2-(231)=0

a = 1; b = 10; c = -231;
Δ = b2-4ac
Δ = 102-4·1·(-231)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-32}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+32}{2*1}=\frac{22}{2}
=11
$