4/2x+1-1/3x+1=5

Solution for 4/2x+1-1/3x+1=5 equation:

4/2x+1-1/3x+1=5

We move all terms to the left:

4/2x+1-1/3x+1-(5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/2x-1/3x-3=0

We calculate fractions


12x/6x^2+(-2x)/6x^2-3=0

We multiply all the terms by the denominator


12x+(-2x)-3*6x^2=0

Wy multiply elements

-18x^2+12x+(-2x)=0

We get rid of parentheses

-18x^2+12x-2x=0

We add all the numbers together, and all the variables

-18x^2+10x=0

a = -18; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-18)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-18}=\frac{-20}{-36}
=5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-18}=\frac{0}{-36}
=0
$