3/x-3/4x=17/8-2

Solution for 3/x-3/4x=17/8-2 equation:

3/x-3/4x=17/8-2

We move all terms to the left:

3/x-3/4x-(17/8-2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/x-3/4x+2-17/8=0

We calculate fractions


(-272x^2)/256x^2+768x/256x^2+(-192x)/256x^2+2=0

We multiply all the terms by the denominator


(-272x^2)+768x+(-192x)+2*256x^2=0

Wy multiply elements

(-272x^2)+512x^2+768x+(-192x)=0

We get rid of parentheses

-272x^2+512x^2+768x-192x=0

We add all the numbers together, and all the variables

240x^2+576x=0

a = 240; b = 576; c = 0;
Δ = b2-4ac
Δ = 5762-4·240·0
Δ = 331776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{331776}=576$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-576}{2*240}=\frac{-1152}{480}
=-2+2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+576}{2*240}=\frac{0}{480}
=0
$