(5x+7)(-6x+8)=0

Solution for (5x+7)(-6x+8)=0 equation:

(5x+7)(-6x+8)=0

We multiply parentheses ..

(-30x^2+40x-42x+56)=0

We get rid of parentheses

-30x^2+40x-42x+56=0

We add all the numbers together, and all the variables

-30x^2-2x+56=0

a = -30; b = -2; c = +56;
Δ = b2-4ac
Δ = -22-4·(-30)·56
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-82}{2*-30}=\frac{-80}{-60}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+82}{2*-30}=\frac{84}{-60}
=-1+2/5
$