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

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

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

We multiply parentheses ..

(+24x^2+56x-9x-21)=0

We get rid of parentheses

24x^2+56x-9x-21=0

We add all the numbers together, and all the variables

24x^2+47x-21=0

a = 24; b = 47; c = -21;
Δ = b2-4ac
Δ = 472-4·24·(-21)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-65}{2*24}=\frac{-112}{48}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+65}{2*24}=\frac{18}{48}
=3/8
$