6x+x*x=180

Solution for 6x+x*x=180 equation:

6x+x*x=180

We move all terms to the left:

6x+x*x-(180)=0

Wy multiply elements

x^2+6x-180=0

a = 1; b = 6; c = -180;
Δ = b2-4ac
Δ = 62-4·1·(-180)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{21}}{2*1}=\frac{-6-6\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{21}}{2*1}=\frac{-6+6\sqrt{21}}{2}
$