(5x-6)(8x+9)=0

Solution for (5x-6)(8x+9)=0 equation:

(5x-6)(8x+9)=0

We multiply parentheses ..

(+40x^2+45x-48x-54)=0

We get rid of parentheses

40x^2+45x-48x-54=0

We add all the numbers together, and all the variables

40x^2-3x-54=0

a = 40; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·40·(-54)
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-93}{2*40}=\frac{-90}{80}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+93}{2*40}=\frac{96}{80}
=1+1/5
$