7x(8x+120)=180

Solution for 7x(8x+120)=180 equation:

7x(8x+120)=180

We move all terms to the left:

7x(8x+120)-(180)=0

We multiply parentheses

56x^2+840x-180=0

a = 56; b = 840; c = -180;
Δ = b2-4ac
Δ = 8402-4·56·(-180)
Δ = 745920
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:

$\sqrt{\Delta}=\sqrt{745920}=\sqrt{576*1295}=\sqrt{576}*\sqrt{1295}=24\sqrt{1295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(840)-24\sqrt{1295}}{2*56}=\frac{-840-24\sqrt{1295}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(840)+24\sqrt{1295}}{2*56}=\frac{-840+24\sqrt{1295}}{112}
$