5/2x=3/8x+2

Solution for 5/2x=3/8x+2 equation:

5/2x=3/8x+2

We move all terms to the left:

5/2x-(3/8x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

5/2x-3/8x-2=0

We calculate fractions


40x/16x^2+(-6x)/16x^2-2=0

We multiply all the terms by the denominator


40x+(-6x)-2*16x^2=0

Wy multiply elements

-32x^2+40x+(-6x)=0

We get rid of parentheses

-32x^2+40x-6x=0

We add all the numbers together, and all the variables

-32x^2+34x=0

a = -32; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-32)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-32}=\frac{-68}{-64}
=1+1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-32}=\frac{0}{-64}
=0
$