10+3/2x=9/8x+4

Solution for 10+3/2x=9/8x+4 equation:

10+3/2x=9/8x+4

We move all terms to the left:

10+3/2x-(9/8x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

3/2x-9/8x-4+10=0

We calculate fractions


24x/16x^2+(-18x)/16x^2-4+10=0

We add all the numbers together, and all the variables

24x/16x^2+(-18x)/16x^2+6=0

We multiply all the terms by the denominator


24x+(-18x)+6*16x^2=0

Wy multiply elements

96x^2+24x+(-18x)=0

We get rid of parentheses

96x^2+24x-18x=0

We add all the numbers together, and all the variables

96x^2+6x=0

a = 96; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·96·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*96}=\frac{-12}{192}
=-1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*96}=\frac{0}{192}
=0
$