x+x^2=131

Solution for x+x^2=131 equation:

x+x^2=131

We move all terms to the left:

x+x^2-(131)=0

a = 1; b = 1; c = -131;
Δ = b2-4ac
Δ = 12-4·1·(-131)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{21}}{2*1}=\frac{-1-5\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{21}}{2*1}=\frac{-1+5\sqrt{21}}{2}
$