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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

45x^2+29x-30=0

a = 45; b = 29; c = -30;
Δ = b2-4ac
Δ = 292-4·45·(-30)
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*45}=\frac{-108}{90}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+79}{2*45}=\frac{50}{90}
=5/9
$