X^2+11x=31

Solution for X^2+11x=31 equation:

X^2+11X=31

We move all terms to the left:

X^2+11X-(31)=0

a = 1; b = 11; c = -31;
Δ = b2-4ac
Δ = 112-4·1·(-31)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7\sqrt{5}}{2*1}=\frac{-11-7\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7\sqrt{5}}{2*1}=\frac{-11+7\sqrt{5}}{2}
$