(3x-65)(2x-20)=180

Solution for (3x-65)(2x-20)=180 equation:

(3x-65)(2x-20)=180

We move all terms to the left:

(3x-65)(2x-20)-(180)=0

We multiply parentheses ..

(+6x^2-60x-130x+1300)-180=0

We get rid of parentheses

6x^2-60x-130x+1300-180=0

We add all the numbers together, and all the variables

6x^2-190x+1120=0

a = 6; b = -190; c = +1120;
Δ = b2-4ac
Δ = -1902-4·6·1120
Δ = 9220
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:

$\sqrt{\Delta}=\sqrt{9220}=\sqrt{4*2305}=\sqrt{4}*\sqrt{2305}=2\sqrt{2305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{2305}}{2*6}=\frac{190-2\sqrt{2305}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{2305}}{2*6}=\frac{190+2\sqrt{2305}}{12}
$