5/2x-2/8x=9

Solution for 5/2x-2/8x=9 equation:

5/2x-2/8x=9

We move all terms to the left:

5/2x-2/8x-(9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


40x/16x^2+(-4x)/16x^2-9=0

We multiply all the terms by the denominator


40x+(-4x)-9*16x^2=0

Wy multiply elements

-144x^2+40x+(-4x)=0

We get rid of parentheses

-144x^2+40x-4x=0

We add all the numbers together, and all the variables

-144x^2+36x=0

a = -144; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-144)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-144}=\frac{-72}{-288}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-144}=\frac{0}{-288}
=0
$