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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

4/x-2/3x-5+3=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-6x^2+12x-2x=0

We add all the numbers together, and all the variables

-6x^2+10x=0

a = -6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-6)·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*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-6}=\frac{0}{-12}
=0
$