6x(x+20)+x=180

Solution for 6x(x+20)+x=180 equation:

6x(x+20)+x=180

We move all terms to the left:

6x(x+20)+x-(180)=0

We add all the numbers together, and all the variables

x+6x(x+20)-180=0

We multiply parentheses

6x^2+x+120x-180=0

We add all the numbers together, and all the variables

6x^2+121x-180=0

a = 6; b = 121; c = -180;
Δ = b2-4ac
Δ = 1212-4·6·(-180)
Δ = 18961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-\sqrt{18961}}{2*6}=\frac{-121-\sqrt{18961}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+\sqrt{18961}}{2*6}=\frac{-121+\sqrt{18961}}{12}
$