-4x+5x(-3x+8)=15

Solution for -4x+5x(-3x+8)=15 equation:

-4x+5x(-3x+8)=15

We move all terms to the left:

-4x+5x(-3x+8)-(15)=0

We multiply parentheses

-15x^2-4x+40x-15=0

We add all the numbers together, and all the variables

-15x^2+36x-15=0

a = -15; b = 36; c = -15;
Δ = b2-4ac
Δ = 362-4·(-15)·(-15)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{11}}{2*-15}=\frac{-36-6\sqrt{11}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{11}}{2*-15}=\frac{-36+6\sqrt{11}}{-30}
$