(4x+1)(9x-3)=180

Solution for (4x+1)(9x-3)=180 equation:

(4x+1)(9x-3)=180

We move all terms to the left:

(4x+1)(9x-3)-(180)=0

We multiply parentheses ..

(+36x^2-12x+9x-3)-180=0

We get rid of parentheses

36x^2-12x+9x-3-180=0

We add all the numbers together, and all the variables

36x^2-3x-183=0

a = 36; b = -3; c = -183;
Δ = b2-4ac
Δ = -32-4·36·(-183)
Δ = 26361
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:

$\sqrt{\Delta}=\sqrt{26361}=\sqrt{9*2929}=\sqrt{9}*\sqrt{2929}=3\sqrt{2929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{2929}}{2*36}=\frac{3-3\sqrt{2929}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{2929}}{2*36}=\frac{3+3\sqrt{2929}}{72}
$