X-2/3x=2,1

Solution for X-2/3x=2,1 equation:

X-2/3X=2.1

We move all terms to the left:

X-2/3X-(2.1)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-2/3X-2.1=0

We multiply all the terms by the denominator


X*3X-(2.1)*3X-2=0

We multiply parentheses

X*3X-6.3X-2=0

Wy multiply elements

3X^2-6.3X-2=0

a = 3; b = -6.3; c = -2;
Δ = b2-4ac
Δ = -6.32-4·3·(-2)
Δ = 63.69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6.3)-\sqrt{63.69}}{2*3}=\frac{6.3-\sqrt{63.69}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.3)+\sqrt{63.69}}{2*3}=\frac{6.3+\sqrt{63.69}}{6}
$