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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2-27x-1x+9)-180=0

We get rid of parentheses

3x^2-27x-1x+9-180=0

We add all the numbers together, and all the variables

3x^2-28x-171=0

a = 3; b = -28; c = -171;
Δ = b2-4ac
Δ = -282-4·3·(-171)
Δ = 2836
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:

$\sqrt{\Delta}=\sqrt{2836}=\sqrt{4*709}=\sqrt{4}*\sqrt{709}=2\sqrt{709}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{709}}{2*3}=\frac{28-2\sqrt{709}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{709}}{2*3}=\frac{28+2\sqrt{709}}{6}
$