14x(4x+50)=180

Solution for 14x(4x+50)=180 equation:

14x(4x+50)=180

We move all terms to the left:

14x(4x+50)-(180)=0

We multiply parentheses

56x^2+700x-180=0

a = 56; b = 700; c = -180;
Δ = b2-4ac
Δ = 7002-4·56·(-180)
Δ = 530320
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:

$\sqrt{\Delta}=\sqrt{530320}=\sqrt{16*33145}=\sqrt{16}*\sqrt{33145}=4\sqrt{33145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(700)-4\sqrt{33145}}{2*56}=\frac{-700-4\sqrt{33145}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(700)+4\sqrt{33145}}{2*56}=\frac{-700+4\sqrt{33145}}{112}
$