(2x-9)(6x+8)=0

Solution for (2x-9)(6x+8)=0 equation:

(2x-9)(6x+8)=0

We multiply parentheses ..

(+12x^2+16x-54x-72)=0

We get rid of parentheses

12x^2+16x-54x-72=0

We add all the numbers together, and all the variables

12x^2-38x-72=0

a = 12; b = -38; c = -72;
Δ = b2-4ac
Δ = -382-4·12·(-72)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-70}{2*12}=\frac{-32}{24}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+70}{2*12}=\frac{108}{24}
=4+1/2
$