(5x-1)(9x+2)=0

Solution for (5x-1)(9x+2)=0 equation:

(5x-1)(9x+2)=0

We multiply parentheses ..

(+45x^2+10x-9x-2)=0

We get rid of parentheses

45x^2+10x-9x-2=0

We add all the numbers together, and all the variables

45x^2+x-2=0

a = 45; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·45·(-2)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*45}=\frac{-20}{90}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*45}=\frac{18}{90}
=1/5
$