6x+x^2=111

Solution for 6x+x^2=111 equation:

6x+x^2=111

We move all terms to the left:

6x+x^2-(111)=0

a = 1; b = 6; c = -111;
Δ = b2-4ac
Δ = 62-4·1·(-111)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{30}}{2*1}=\frac{-6-4\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{30}}{2*1}=\frac{-6+4\sqrt{30}}{2}
$