X/3x-10+8x=100

Solution for X/3x-10+8x=100 equation:

X/3X-10+8X=100

We move all terms to the left:

X/3X-10+8X-(100)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

8X+X/3X-110=0

We multiply all the terms by the denominator


8X*3X+X-110*3X=0

We add all the numbers together, and all the variables

X+8X*3X-110*3X=0

Wy multiply elements

24X^2+X-330X=0

We add all the numbers together, and all the variables

24X^2-329X=0

a = 24; b = -329; c = 0;
Δ = b2-4ac
Δ = -3292-4·24·0
Δ = 108241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{108241}=329$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-329)-329}{2*24}=\frac{0}{48}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-329)+329}{2*24}=\frac{658}{48}
=13+17/24
$