X+2/3x=100

Solution for X+2/3x=100 equation:

X+2/3X=100

We move all terms to the left:

X+2/3X-(100)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-100*3X+2=0

Wy multiply elements

3X^2-300X+2=0

a = 3; b = -300; c = +2;
Δ = b2-4ac
Δ = -3002-4·3·2
Δ = 89976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{89976}=\sqrt{4*22494}=\sqrt{4}*\sqrt{22494}=2\sqrt{22494}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22494}}{2*3}=\frac{300-2\sqrt{22494}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22494}}{2*3}=\frac{300+2\sqrt{22494}}{6}
$