4x/x+8=x+2/x+3

Solution for 4x/x+8=x+2/x+3 equation:

4x/x+8=x+2/x+3

We move all terms to the left:

4x/x+8-(x+2/x+3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

4x/x-x-2/x-3+8=0

We multiply all the terms by the denominator


4x-x*x-3*x+8*x-2=0

We add all the numbers together, and all the variables

9x-x*x-2=0

Wy multiply elements

-1x^2+9x-2=0

a = -1; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·(-1)·(-2)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{73}}{2*-1}=\frac{-9-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*-1}=\frac{-9+\sqrt{73}}{-2}
$