6x+21+x2+2x=180

Solution for 6x+21+x2+2x=180 equation:

6x+21+x2+2x=180

We move all terms to the left:

6x+21+x2+2x-(180)=0

We add all the numbers together, and all the variables

x^2+8x-159=0

a = 1; b = 8; c = -159;
Δ = b2-4ac
Δ = 82-4·1·(-159)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10\sqrt{7}}{2*1}=\frac{-8-10\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10\sqrt{7}}{2*1}=\frac{-8+10\sqrt{7}}{2}
$