(8x+9)(3x-13)=0

Solution for (8x+9)(3x-13)=0 equation:

(8x+9)(3x-13)=0

We multiply parentheses ..

(+24x^2-104x+27x-117)=0

We get rid of parentheses

24x^2-104x+27x-117=0

We add all the numbers together, and all the variables

24x^2-77x-117=0

a = 24; b = -77; c = -117;
Δ = b2-4ac
Δ = -772-4·24·(-117)
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-131}{2*24}=\frac{-54}{48}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+131}{2*24}=\frac{208}{48}
=4+1/3
$