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

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

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

We multiply parentheses ..

(+12x^2-21x+28x-49)=0

We get rid of parentheses

12x^2-21x+28x-49=0

We add all the numbers together, and all the variables

12x^2+7x-49=0

a = 12; b = 7; c = -49;
Δ = b2-4ac
Δ = 72-4·12·(-49)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-49}{2*12}=\frac{-56}{24}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+49}{2*12}=\frac{42}{24}
=1+3/4
$