(3x+4)(9x-1)=0

Solution for (3x+4)(9x-1)=0 equation:

(3x+4)(9x-1)=0

We multiply parentheses ..

(+27x^2-3x+36x-4)=0

We get rid of parentheses

27x^2-3x+36x-4=0

We add all the numbers together, and all the variables

27x^2+33x-4=0

a = 27; b = 33; c = -4;
Δ = b2-4ac
Δ = 332-4·27·(-4)
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{-(33)-39}{2*27}=\frac{-72}{54}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+39}{2*27}=\frac{6}{54}
=1/9
$