-5x(3x-8)=-15x-40

Solution for -5x(3x-8)=-15x-40 equation:

-5x(3x-8)=-15x-40

We move all terms to the left:

-5x(3x-8)-(-15x-40)=0

We multiply parentheses

-15x^2+40x-(-15x-40)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-15x^2+55x+40=0

a = -15; b = 55; c = +40;
Δ = b2-4ac
Δ = 552-4·(-15)·40
Δ = 5425
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:

$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{217}}{2*-15}=\frac{-55-5\sqrt{217}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{217}}{2*-15}=\frac{-55+5\sqrt{217}}{-30}
$