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

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

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

We add all the numbers together, and all the variables

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