21/8x+30=51/3x

Solution for 21/8x+30=51/3x equation:

21/8x+30=51/3x

We move all terms to the left:

21/8x+30-(51/3x)=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

21/8x-(+51/3x)+30=0

We get rid of parentheses

21/8x-51/3x+30=0

We calculate fractions


63x/24x^2+(-408x)/24x^2+30=0

We multiply all the terms by the denominator


63x+(-408x)+30*24x^2=0

Wy multiply elements

720x^2+63x+(-408x)=0

We get rid of parentheses

720x^2+63x-408x=0

We add all the numbers together, and all the variables

720x^2-345x=0

a = 720; b = -345; c = 0;
Δ = b2-4ac
Δ = -3452-4·720·0
Δ = 119025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{119025}=345$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-345)-345}{2*720}=\frac{0}{1440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-345)+345}{2*720}=\frac{690}{1440}
=23/48
$