5x/x+4=3x+1

Solution for 5x/x+4=3x+1 equation:

5x/x+4=3x+1

We move all terms to the left:

5x/x+4-(3x+1)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

5x/x-3x-1+4=0

We multiply all the terms by the denominator


5x-3x*x-1*x+4*x=0

We add all the numbers together, and all the variables

8x-3x*x=0

Wy multiply elements

-3x^2+8x=0

a = -3; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-3)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-3}=\frac{-16}{-6}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-3}=\frac{0}{-6}
=0
$