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

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

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

We multiply parentheses ..

(+30x^2+25x-54x-45)=0

We get rid of parentheses

30x^2+25x-54x-45=0

We add all the numbers together, and all the variables

30x^2-29x-45=0

a = 30; b = -29; c = -45;
Δ = b2-4ac
Δ = -292-4·30·(-45)
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-79}{2*30}=\frac{-50}{60}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+79}{2*30}=\frac{108}{60}
=1+4/5
$