(9x-6)(5x+1)=0

Solution for (9x-6)(5x+1)=0 equation:

(9x-6)(5x+1)=0

We multiply parentheses ..

(+45x^2+9x-30x-6)=0

We get rid of parentheses

45x^2+9x-30x-6=0

We add all the numbers together, and all the variables

45x^2-21x-6=0

a = 45; b = -21; c = -6;
Δ = b2-4ac
Δ = -212-4·45·(-6)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-39}{2*45}=\frac{-18}{90}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+39}{2*45}=\frac{60}{90}
=2/3
$