(6x-8)(8x+3)=0

Solution for (6x-8)(8x+3)=0 equation:

(6x-8)(8x+3)=0

We multiply parentheses ..

(+48x^2+18x-64x-24)=0

We get rid of parentheses

48x^2+18x-64x-24=0

We add all the numbers together, and all the variables

48x^2-46x-24=0

a = 48; b = -46; c = -24;
Δ = b2-4ac
Δ = -462-4·48·(-24)
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{-(-46)-82}{2*48}=\frac{-36}{96}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+82}{2*48}=\frac{128}{96}
=1+1/3
$