(3x+14)x=180

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

(3x+14)x=180

We move all terms to the left:

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

We multiply parentheses

3x^2+14x-180=0

a = 3; b = 14; c = -180;
Δ = b2-4ac
Δ = 142-4·3·(-180)
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{589}}{2*3}=\frac{-14-2\sqrt{589}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{589}}{2*3}=\frac{-14+2\sqrt{589}}{6}
$