-6x(x-5)+5(8x-3)=15

Solution for -6x(x-5)+5(8x-3)=15 equation:

-6x(x-5)+5(8x-3)=15

We move all terms to the left:

-6x(x-5)+5(8x-3)-(15)=0

We multiply parentheses

-6x^2+30x+40x-15-15=0

We add all the numbers together, and all the variables

-6x^2+70x-30=0

a = -6; b = 70; c = -30;
Δ = b2-4ac
Δ = 702-4·(-6)·(-30)
Δ = 4180
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:

$\sqrt{\Delta}=\sqrt{4180}=\sqrt{4*1045}=\sqrt{4}*\sqrt{1045}=2\sqrt{1045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1045}}{2*-6}=\frac{-70-2\sqrt{1045}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1045}}{2*-6}=\frac{-70+2\sqrt{1045}}{-12}
$