(3x-7)(9x+4)=0

Solution for (3x-7)(9x+4)=0 equation:

(3x-7)(9x+4)=0

We multiply parentheses ..

(+27x^2+12x-63x-28)=0

We get rid of parentheses

27x^2+12x-63x-28=0

We add all the numbers together, and all the variables

27x^2-51x-28=0

a = 27; b = -51; c = -28;
Δ = b2-4ac
Δ = -512-4·27·(-28)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-75}{2*27}=\frac{-24}{54}
=-4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+75}{2*27}=\frac{126}{54}
=2+1/3
$