(3x-5)(2x-8)=360

Solution for (3x-5)(2x-8)=360 equation:

(3x-5)(2x-8)=360

We move all terms to the left:

(3x-5)(2x-8)-(360)=0

We multiply parentheses ..

(+6x^2-24x-10x+40)-360=0

We get rid of parentheses

6x^2-24x-10x+40-360=0

We add all the numbers together, and all the variables

6x^2-34x-320=0

a = 6; b = -34; c = -320;
Δ = b2-4ac
Δ = -342-4·6·(-320)
Δ = 8836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8836}=94$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-94}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+94}{2*6}=\frac{128}{12}
=10+2/3
$