4/x=17/8x-3

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

4/x=17/8x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 8x-3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


32x/8x^2+(-17x)/8x^2+3=0

We multiply all the terms by the denominator


32x+(-17x)+3*8x^2=0

Wy multiply elements

24x^2+32x+(-17x)=0

We get rid of parentheses

24x^2+32x-17x=0

We add all the numbers together, and all the variables

24x^2+15x=0

a = 24; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·24·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*24}=\frac{-30}{48}
=-5/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*24}=\frac{0}{48}
=0
$