14x(15+x)=180

Solution for 14x(15+x)=180 equation:

14x(15+x)=180

We move all terms to the left:

14x(15+x)-(180)=0

We add all the numbers together, and all the variables

14x(x+15)-180=0

We multiply parentheses

14x^2+210x-180=0

a = 14; b = 210; c = -180;
Δ = b2-4ac
Δ = 2102-4·14·(-180)
Δ = 54180
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:

$\sqrt{\Delta}=\sqrt{54180}=\sqrt{36*1505}=\sqrt{36}*\sqrt{1505}=6\sqrt{1505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(210)-6\sqrt{1505}}{2*14}=\frac{-210-6\sqrt{1505}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(210)+6\sqrt{1505}}{2*14}=\frac{-210+6\sqrt{1505}}{28}
$