5x/3x-4=5+7x

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

5x/3x-4=5+7x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5x/3x-7x-5-4=0

We multiply all the terms by the denominator


5x-7x*3x-5*3x-4*3x=0

Wy multiply elements

-21x^2+5x-15x-12x=0

We add all the numbers together, and all the variables

-21x^2-22x=0

a = -21; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-21)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-21}=\frac{44}{-42}
=-1+1/21
$