3x(7x+4)=3x(5x-4)

Solution for 3x(7x+4)=3x(5x-4) equation:

3x(7x+4)=3x(5x-4)

We move all terms to the left:

3x(7x+4)-(3x(5x-4))=0

We multiply parentheses

21x^2+12x-(3x(5x-4))=0


We calculate terms in parentheses: -(3x(5x-4)), so:

3x(5x-4)

We multiply parentheses

15x^2-12x

Back to the equation:

-(15x^2-12x)


We get rid of parentheses

21x^2-15x^2+12x+12x=0

We add all the numbers together, and all the variables

6x^2+24x=0

a = 6; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·6·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*6}=\frac{-48}{12}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*6}=\frac{0}{12}
=0
$