(4x+3)(5x-8)=0

Solution for (4x+3)(5x-8)=0 equation:

(4x+3)(5x-8)=0

We multiply parentheses ..

(+20x^2-32x+15x-24)=0

We get rid of parentheses

20x^2-32x+15x-24=0

We add all the numbers together, and all the variables

20x^2-17x-24=0

a = 20; b = -17; c = -24;
Δ = b2-4ac
Δ = -172-4·20·(-24)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-47}{2*20}=\frac{-30}{40}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+47}{2*20}=\frac{64}{40}
=1+3/5
$