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

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

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

We multiply parentheses ..

(+40x^2+35x-24x-21)=0

We get rid of parentheses

40x^2+35x-24x-21=0

We add all the numbers together, and all the variables

40x^2+11x-21=0

a = 40; b = 11; c = -21;
Δ = b2-4ac
Δ = 112-4·40·(-21)
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*40}=\frac{-70}{80}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+59}{2*40}=\frac{48}{80}
=3/5
$