5/8x+30=10+1/3x

Solution for 5/8x+30=10+1/3x equation:

5/8x+30=10+1/3x

We move all terms to the left:

5/8x+30-(10+1/3x)=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

5/8x-(1/3x+10)+30=0

We get rid of parentheses

5/8x-1/3x-10+30=0

We calculate fractions


15x/24x^2+(-8x)/24x^2-10+30=0

We add all the numbers together, and all the variables

15x/24x^2+(-8x)/24x^2+20=0

We multiply all the terms by the denominator


15x+(-8x)+20*24x^2=0

Wy multiply elements

480x^2+15x+(-8x)=0

We get rid of parentheses

480x^2+15x-8x=0

We add all the numbers together, and all the variables

480x^2+7x=0

a = 480; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·480·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*480}=\frac{-14}{960}
=-7/480
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*480}=\frac{0}{960}
=0
$