(3x+7)(9x-43)=180

Solution for (3x+7)(9x-43)=180 equation:

(3x+7)(9x-43)=180

We move all terms to the left:

(3x+7)(9x-43)-(180)=0

We multiply parentheses ..

(+27x^2-129x+63x-301)-180=0

We get rid of parentheses

27x^2-129x+63x-301-180=0

We add all the numbers together, and all the variables

27x^2-66x-481=0

a = 27; b = -66; c = -481;
Δ = b2-4ac
Δ = -662-4·27·(-481)
Δ = 56304
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:

$\sqrt{\Delta}=\sqrt{56304}=\sqrt{144*391}=\sqrt{144}*\sqrt{391}=12\sqrt{391}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-12\sqrt{391}}{2*27}=\frac{66-12\sqrt{391}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+12\sqrt{391}}{2*27}=\frac{66+12\sqrt{391}}{54}
$