x+x^2=2990

Solution for x+x^2=2990 equation:

x+x^2=2990

We move all terms to the left:

x+x^2-(2990)=0

a = 1; b = 1; c = -2990;
Δ = b2-4ac
Δ = 12-4·1·(-2990)
Δ = 11961
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:

$\sqrt{\Delta}=\sqrt{11961}=\sqrt{9*1329}=\sqrt{9}*\sqrt{1329}=3\sqrt{1329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{1329}}{2*1}=\frac{-1-3\sqrt{1329}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{1329}}{2*1}=\frac{-1+3\sqrt{1329}}{2}
$