(5x+9)(8x-9)=0

Solution for (5x+9)(8x-9)=0 equation:

(5x+9)(8x-9)=0

We multiply parentheses ..

(+40x^2-45x+72x-81)=0

We get rid of parentheses

40x^2-45x+72x-81=0

We add all the numbers together, and all the variables

40x^2+27x-81=0

a = 40; b = 27; c = -81;
Δ = b2-4ac
Δ = 272-4·40·(-81)
Δ = 13689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13689}=117$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-117}{2*40}=\frac{-144}{80}
=-1+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+117}{2*40}=\frac{90}{80}
=1+1/8
$