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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+9x^2-43x+27x-129)-180=0

We get rid of parentheses

9x^2-43x+27x-129-180=0

We add all the numbers together, and all the variables

9x^2-16x-309=0

a = 9; b = -16; c = -309;
Δ = b2-4ac
Δ = -162-4·9·(-309)
Δ = 11380
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:

$\sqrt{\Delta}=\sqrt{11380}=\sqrt{4*2845}=\sqrt{4}*\sqrt{2845}=2\sqrt{2845}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{2845}}{2*9}=\frac{16-2\sqrt{2845}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{2845}}{2*9}=\frac{16+2\sqrt{2845}}{18}
$