17/8x+30=16/3x

Solution for 17/8x+30=16/3x equation:

17/8x+30=16/3x

We move all terms to the left:

17/8x+30-(16/3x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

17/8x-(+16/3x)+30=0

We get rid of parentheses

17/8x-16/3x+30=0

We calculate fractions


51x/24x^2+(-128x)/24x^2+30=0

We multiply all the terms by the denominator


51x+(-128x)+30*24x^2=0

Wy multiply elements

720x^2+51x+(-128x)=0

We get rid of parentheses

720x^2+51x-128x=0

We add all the numbers together, and all the variables

720x^2-77x=0

a = 720; b = -77; c = 0;
Δ = b2-4ac
Δ = -772-4·720·0
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-77}{2*720}=\frac{0}{1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+77}{2*720}=\frac{154}{1440}
=77/720
$