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

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

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

We move all terms to the left:

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

We multiply parentheses

20x^2+16x-(3x(7x+4))=0


We calculate terms in parentheses: -(3x(7x+4)), so:

3x(7x+4)

We multiply parentheses

21x^2+12x

Back to the equation:

-(21x^2+12x)


We get rid of parentheses

20x^2-21x^2+16x-12x=0

We add all the numbers together, and all the variables

-1x^2+4x=0

a = -1; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-1}=\frac{-8}{-2}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-1}=\frac{0}{-2}
=0
$