4/x+3=9/8x+2

Solution for 4/x+3=9/8x+2 equation:

4/x+3=9/8x+2

We move all terms to the left:

4/x+3-(9/8x+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

4/x-9/8x-2+3=0

We calculate fractions


32x/8x^2+(-9x)/8x^2-2+3=0

We add all the numbers together, and all the variables

32x/8x^2+(-9x)/8x^2+1=0

We multiply all the terms by the denominator


32x+(-9x)+1*8x^2=0

Wy multiply elements

8x^2+32x+(-9x)=0

We get rid of parentheses

8x^2+32x-9x=0

We add all the numbers together, and all the variables

8x^2+23x=0

a = 8; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·8·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*8}=\frac{-46}{16}
=-2+7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*8}=\frac{0}{16}
=0
$