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

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

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

We multiply parentheses ..

(+40x^2-15x+64x-24)=0

We get rid of parentheses

40x^2-15x+64x-24=0

We add all the numbers together, and all the variables

40x^2+49x-24=0

a = 40; b = 49; c = -24;
Δ = b2-4ac
Δ = 492-4·40·(-24)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-79}{2*40}=\frac{-128}{80}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+79}{2*40}=\frac{30}{80}
=3/8
$