7x(x+9)=180

Solution for 7x(x+9)=180 equation:

7x(x+9)=180

We move all terms to the left:

7x(x+9)-(180)=0

We multiply parentheses

7x^2+63x-180=0

a = 7; b = 63; c = -180;
Δ = b2-4ac
Δ = 632-4·7·(-180)
Δ = 9009
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:

$\sqrt{\Delta}=\sqrt{9009}=\sqrt{9*1001}=\sqrt{9}*\sqrt{1001}=3\sqrt{1001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{1001}}{2*7}=\frac{-63-3\sqrt{1001}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{1001}}{2*7}=\frac{-63+3\sqrt{1001}}{14}
$