(-3x-7)(-5x+8)=0

Solution for (-3x-7)(-5x+8)=0 equation:

(-3x-7)(-5x+8)=0

We multiply parentheses ..

(+15x^2-24x+35x-56)=0

We get rid of parentheses

15x^2-24x+35x-56=0

We add all the numbers together, and all the variables

15x^2+11x-56=0

a = 15; b = 11; c = -56;
Δ = b2-4ac
Δ = 112-4·15·(-56)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-59}{2*15}=\frac{-70}{30}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+59}{2*15}=\frac{48}{30}
=1+3/5
$