x+(6x+10)(x+2)=180

Solution for x+(6x+10)(x+2)=180 equation:

x+(6x+10)(x+2)=180

We move all terms to the left:

x+(6x+10)(x+2)-(180)=0

We multiply parentheses ..

(+6x^2+12x+10x+20)+x-180=0

We get rid of parentheses

6x^2+12x+10x+x+20-180=0

We add all the numbers together, and all the variables

6x^2+23x-160=0

a = 6; b = 23; c = -160;
Δ = b2-4ac
Δ = 232-4·6·(-160)
Δ = 4369
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{-(23)-\sqrt{4369}}{2*6}=\frac{-23-\sqrt{4369}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{4369}}{2*6}=\frac{-23+\sqrt{4369}}{12}
$