(5x-9)(6x+2)=0

Solution for (5x-9)(6x+2)=0 equation:

(5x-9)(6x+2)=0

We multiply parentheses ..

(+30x^2+10x-54x-18)=0

We get rid of parentheses

30x^2+10x-54x-18=0

We add all the numbers together, and all the variables

30x^2-44x-18=0

a = 30; b = -44; c = -18;
Δ = b2-4ac
Δ = -442-4·30·(-18)
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-64}{2*30}=\frac{-20}{60}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+64}{2*30}=\frac{108}{60}
=1+4/5
$