x(6x+42)=36x+180

Solution for x(6x+42)=36x+180 equation:

x(6x+42)=36x+180

We move all terms to the left:

x(6x+42)-(36x+180)=0

We multiply parentheses

6x^2+42x-(36x+180)=0

We get rid of parentheses

6x^2+42x-36x-180=0

We add all the numbers together, and all the variables

6x^2+6x-180=0

a = 6; b = 6; c = -180;
Δ = b2-4ac
Δ = 62-4·6·(-180)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-66}{2*6}=\frac{-72}{12}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+66}{2*6}=\frac{60}{12}
=5
$