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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+(-3x-8)(5x+3)=0

We multiply parentheses ..

(-15x^2-9x-40x-24)-1x=0

We get rid of parentheses

-15x^2-9x-40x-1x-24=0

We add all the numbers together, and all the variables

-15x^2-50x-24=0

a = -15; b = -50; c = -24;
Δ = b2-4ac
Δ = -502-4·(-15)·(-24)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{265}}{2*-15}=\frac{50-2\sqrt{265}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{265}}{2*-15}=\frac{50+2\sqrt{265}}{-30}
$