(4x-6)(3x+8)=0

Solution for (4x-6)(3x+8)=0 equation:

(4x-6)(3x+8)=0

We multiply parentheses ..

(+12x^2+32x-18x-48)=0

We get rid of parentheses

12x^2+32x-18x-48=0

We add all the numbers together, and all the variables

12x^2+14x-48=0

a = 12; b = 14; c = -48;
Δ = b2-4ac
Δ = 142-4·12·(-48)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-50}{2*12}=\frac{-64}{24}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+50}{2*12}=\frac{36}{24}
=1+1/2
$