(3x+2)(9x-7)=0

Solution for (3x+2)(9x-7)=0 equation:

(3x+2)(9x-7)=0

We multiply parentheses ..

(+27x^2-21x+18x-14)=0

We get rid of parentheses

27x^2-21x+18x-14=0

We add all the numbers together, and all the variables

27x^2-3x-14=0

a = 27; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·27·(-14)
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{-(-3)-39}{2*27}=\frac{-36}{54}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+39}{2*27}=\frac{42}{54}
=7/9
$