(3x-7)(9x+3)=0

Solution for (3x-7)(9x+3)=0 equation:

(3x-7)(9x+3)=0

We multiply parentheses ..

(+27x^2+9x-63x-21)=0

We get rid of parentheses

27x^2+9x-63x-21=0

We add all the numbers together, and all the variables

27x^2-54x-21=0

a = 27; b = -54; c = -21;
Δ = b2-4ac
Δ = -542-4·27·(-21)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-72}{2*27}=\frac{-18}{54}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+72}{2*27}=\frac{126}{54}
=2+1/3
$