(2x+9)(3x-8)=0

Solution for (2x+9)(3x-8)=0 equation:

(2x+9)(3x-8)=0

We multiply parentheses ..

(+6x^2-16x+27x-72)=0

We get rid of parentheses

6x^2-16x+27x-72=0

We add all the numbers together, and all the variables

6x^2+11x-72=0

a = 6; b = 11; c = -72;
Δ = b2-4ac
Δ = 112-4·6·(-72)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-43}{2*6}=\frac{-54}{12}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+43}{2*6}=\frac{32}{12}
=2+2/3
$