(6x-8)*(7x+3)=0

Solution for (6x-8)*(7x+3)=0 equation:

(6x-8)(7x+3)=0

We multiply parentheses ..

(+42x^2+18x-56x-24)=0

We get rid of parentheses

42x^2+18x-56x-24=0

We add all the numbers together, and all the variables

42x^2-38x-24=0

a = 42; b = -38; c = -24;
Δ = b2-4ac
Δ = -382-4·42·(-24)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-74}{2*42}=\frac{-36}{84}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+74}{2*42}=\frac{112}{84}
=1+1/3
$