8x(15-5x)-6=39

Solution for 8x(15-5x)-6=39 equation:

8x(15-5x)-6=39

We move all terms to the left:

8x(15-5x)-6-(39)=0

We add all the numbers together, and all the variables

8x(-5x+15)-6-39=0

We add all the numbers together, and all the variables

8x(-5x+15)-45=0

We multiply parentheses

-40x^2+120x-45=0

a = -40; b = 120; c = -45;
Δ = b2-4ac
Δ = 1202-4·(-40)·(-45)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-60\sqrt{2}}{2*-40}=\frac{-120-60\sqrt{2}}{-80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+60\sqrt{2}}{2*-40}=\frac{-120+60\sqrt{2}}{-80}
$