(3x-5)(9x+3)=0

Solution for (3x-5)(9x+3)=0 equation:

(3x-5)(9x+3)=0

We multiply parentheses ..

(+27x^2+9x-45x-15)=0

We get rid of parentheses

27x^2+9x-45x-15=0

We add all the numbers together, and all the variables

27x^2-36x-15=0

a = 27; b = -36; c = -15;
Δ = b2-4ac
Δ = -362-4·27·(-15)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-54}{2*27}=\frac{-18}{54}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+54}{2*27}=\frac{90}{54}
=1+2/3
$