6x+x^2=114

Solution for 6x+x^2=114 equation:

6x+x^2=114

We move all terms to the left:

6x+x^2-(114)=0

a = 1; b = 6; c = -114;
Δ = b2-4ac
Δ = 62-4·1·(-114)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{123}}{2*1}=\frac{-6-2\sqrt{123}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{123}}{2*1}=\frac{-6+2\sqrt{123}}{2}
$