(6x-4)(8x+9)=0

Solution for (6x-4)(8x+9)=0 equation:

(6x-4)(8x+9)=0

We multiply parentheses ..

(+48x^2+54x-32x-36)=0

We get rid of parentheses

48x^2+54x-32x-36=0

We add all the numbers together, and all the variables

48x^2+22x-36=0

a = 48; b = 22; c = -36;
Δ = b2-4ac
Δ = 222-4·48·(-36)
Δ = 7396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7396}=86$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-86}{2*48}=\frac{-108}{96}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+86}{2*48}=\frac{64}{96}
=2/3
$