(3x-13)(x-3)=180

Solution for (3x-13)(x-3)=180 equation:

(3x-13)(x-3)=180

We move all terms to the left:

(3x-13)(x-3)-(180)=0

We multiply parentheses ..

(+3x^2-9x-13x+39)-180=0

We get rid of parentheses

3x^2-9x-13x+39-180=0

We add all the numbers together, and all the variables

3x^2-22x-141=0

a = 3; b = -22; c = -141;
Δ = b2-4ac
Δ = -222-4·3·(-141)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8\sqrt{34}}{2*3}=\frac{22-8\sqrt{34}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8\sqrt{34}}{2*3}=\frac{22+8\sqrt{34}}{6}
$