5x(3x+14)=180

Solution for 5x(3x+14)=180 equation:

5x(3x+14)=180

We move all terms to the left:

5x(3x+14)-(180)=0

We multiply parentheses

15x^2+70x-180=0

a = 15; b = 70; c = -180;
Δ = b2-4ac
Δ = 702-4·15·(-180)
Δ = 15700
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:

$\sqrt{\Delta}=\sqrt{15700}=\sqrt{100*157}=\sqrt{100}*\sqrt{157}=10\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{157}}{2*15}=\frac{-70-10\sqrt{157}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{157}}{2*15}=\frac{-70+10\sqrt{157}}{30}
$