(3x-7)(9x+1)=0

Solution for (3x-7)(9x+1)=0 equation:

(3x-7)(9x+1)=0

We multiply parentheses ..

(+27x^2+3x-63x-7)=0

We get rid of parentheses

27x^2+3x-63x-7=0

We add all the numbers together, and all the variables

27x^2-60x-7=0

a = 27; b = -60; c = -7;
Δ = b2-4ac
Δ = -602-4·27·(-7)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-66}{2*27}=\frac{-6}{54}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+66}{2*27}=\frac{126}{54}
=2+1/3
$