6x+x^2=169

Solution for 6x+x^2=169 equation:

6x+x^2=169

We move all terms to the left:

6x+x^2-(169)=0

a = 1; b = 6; c = -169;
Δ = b2-4ac
Δ = 62-4·1·(-169)
Δ = 712
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:

$\sqrt{\Delta}=\sqrt{712}=\sqrt{4*178}=\sqrt{4}*\sqrt{178}=2\sqrt{178}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{178}}{2*1}=\frac{-6-2\sqrt{178}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{178}}{2*1}=\frac{-6+2\sqrt{178}}{2}
$