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 = 90024
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:

$\sqrt{\Delta}=\sqrt{90024}=\sqrt{484*186}=\sqrt{484}*\sqrt{186}=22\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-22\sqrt{186}}{2*3}=\frac{300-22\sqrt{186}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+22\sqrt{186}}{2*3}=\frac{300+22\sqrt{186}}{6}
$