4x(x+35)=180

Solution for 4x(x+35)=180 equation:

4x(x+35)=180

We move all terms to the left:

4x(x+35)-(180)=0

We multiply parentheses

4x^2+140x-180=0

a = 4; b = 140; c = -180;
Δ = b2-4ac
Δ = 1402-4·4·(-180)
Δ = 22480
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:

$\sqrt{\Delta}=\sqrt{22480}=\sqrt{16*1405}=\sqrt{16}*\sqrt{1405}=4\sqrt{1405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{1405}}{2*4}=\frac{-140-4\sqrt{1405}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{1405}}{2*4}=\frac{-140+4\sqrt{1405}}{8}
$