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

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

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

We multiply parentheses ..

(+21x^2+27x-28x-36)=0

We get rid of parentheses

21x^2+27x-28x-36=0

We add all the numbers together, and all the variables

21x^2-1x-36=0

a = 21; b = -1; c = -36;
Δ = b2-4ac
Δ = -12-4·21·(-36)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-55}{2*21}=\frac{-54}{42}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+55}{2*21}=\frac{56}{42}
=1+1/3
$