(3x+4)(7x-8)=0

Solution for (3x+4)(7x-8)=0 equation:

(3x+4)(7x-8)=0

We multiply parentheses ..

(+21x^2-24x+28x-32)=0

We get rid of parentheses

21x^2-24x+28x-32=0

We add all the numbers together, and all the variables

21x^2+4x-32=0

a = 21; b = 4; c = -32;
Δ = b2-4ac
Δ = 42-4·21·(-32)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-52}{2*21}=\frac{-56}{42}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+52}{2*21}=\frac{48}{42}
=1+1/7
$