5x(3x+50)=180

Solution for 5x(3x+50)=180 equation:

5x(3x+50)=180

We move all terms to the left:

5x(3x+50)-(180)=0

We multiply parentheses

15x^2+250x-180=0

a = 15; b = 250; c = -180;
Δ = b2-4ac
Δ = 2502-4·15·(-180)
Δ = 73300
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:

$\sqrt{\Delta}=\sqrt{73300}=\sqrt{100*733}=\sqrt{100}*\sqrt{733}=10\sqrt{733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-10\sqrt{733}}{2*15}=\frac{-250-10\sqrt{733}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+10\sqrt{733}}{2*15}=\frac{-250+10\sqrt{733}}{30}
$