7x(4x+27)=180

Solution for 7x(4x+27)=180 equation:

7x(4x+27)=180

We move all terms to the left:

7x(4x+27)-(180)=0

We multiply parentheses

28x^2+189x-180=0

a = 28; b = 189; c = -180;
Δ = b2-4ac
Δ = 1892-4·28·(-180)
Δ = 55881
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:

$\sqrt{\Delta}=\sqrt{55881}=\sqrt{9*6209}=\sqrt{9}*\sqrt{6209}=3\sqrt{6209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-3\sqrt{6209}}{2*28}=\frac{-189-3\sqrt{6209}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+3\sqrt{6209}}{2*28}=\frac{-189+3\sqrt{6209}}{56}
$