7x(x-20)=180

Solution for 7x(x-20)=180 equation:

7x(x-20)=180

We move all terms to the left:

7x(x-20)-(180)=0

We multiply parentheses

7x^2-140x-180=0

a = 7; b = -140; c = -180;
Δ = b2-4ac
Δ = -1402-4·7·(-180)
Δ = 24640
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:

$\sqrt{\Delta}=\sqrt{24640}=\sqrt{64*385}=\sqrt{64}*\sqrt{385}=8\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-8\sqrt{385}}{2*7}=\frac{140-8\sqrt{385}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+8\sqrt{385}}{2*7}=\frac{140+8\sqrt{385}}{14}
$