4x+6(x+4)(5x+10)=180

Solution for 4x+6(x+4)(5x+10)=180 equation:

4x+6(x+4)(5x+10)=180

We move all terms to the left:

4x+6(x+4)(5x+10)-(180)=0

We multiply parentheses ..

6(+5x^2+10x+20x+40)+4x-180=0

We multiply parentheses

30x^2+60x+120x+4x+240-180=0

We add all the numbers together, and all the variables

30x^2+184x+60=0

a = 30; b = 184; c = +60;
Δ = b2-4ac
Δ = 1842-4·30·60
Δ = 26656
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:

$\sqrt{\Delta}=\sqrt{26656}=\sqrt{784*34}=\sqrt{784}*\sqrt{34}=28\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(184)-28\sqrt{34}}{2*30}=\frac{-184-28\sqrt{34}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(184)+28\sqrt{34}}{2*30}=\frac{-184+28\sqrt{34}}{60}
$