7x(5x+30)=180

Solution for 7x(5x+30)=180 equation:

7x(5x+30)=180

We move all terms to the left:

7x(5x+30)-(180)=0

We multiply parentheses

35x^2+210x-180=0

a = 35; b = 210; c = -180;
Δ = b2-4ac
Δ = 2102-4·35·(-180)
Δ = 69300
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:

$\sqrt{\Delta}=\sqrt{69300}=\sqrt{900*77}=\sqrt{900}*\sqrt{77}=30\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-30\sqrt{77}}{2*35}=\frac{-210-30\sqrt{77}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+30\sqrt{77}}{2*35}=\frac{-210+30\sqrt{77}}{70}
$