(6x-8)(5x-15)=180

Solution for (6x-8)(5x-15)=180 equation:

(6x-8)(5x-15)=180

We move all terms to the left:

(6x-8)(5x-15)-(180)=0

We multiply parentheses ..

(+30x^2-90x-40x+120)-180=0

We get rid of parentheses

30x^2-90x-40x+120-180=0

We add all the numbers together, and all the variables

30x^2-130x-60=0

a = 30; b = -130; c = -60;
Δ = b2-4ac
Δ = -1302-4·30·(-60)
Δ = 24100
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:

$\sqrt{\Delta}=\sqrt{24100}=\sqrt{100*241}=\sqrt{100}*\sqrt{241}=10\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-10\sqrt{241}}{2*30}=\frac{130-10\sqrt{241}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+10\sqrt{241}}{2*30}=\frac{130+10\sqrt{241}}{60}
$