4x(x+25)=180

Solution for 4x(x+25)=180 equation:

4x(x+25)=180

We move all terms to the left:

4x(x+25)-(180)=0

We multiply parentheses

4x^2+100x-180=0

a = 4; b = 100; c = -180;
Δ = b2-4ac
Δ = 1002-4·4·(-180)
Δ = 12880
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:

$\sqrt{\Delta}=\sqrt{12880}=\sqrt{16*805}=\sqrt{16}*\sqrt{805}=4\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{805}}{2*4}=\frac{-100-4\sqrt{805}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{805}}{2*4}=\frac{-100+4\sqrt{805}}{8}
$