X-2/3x=43

Solution for X-2/3x=43 equation:

X-2/3X=43

We move all terms to the left:

X-2/3X-(43)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-43*3X-2=0

Wy multiply elements

3X^2-129X-2=0

a = 3; b = -129; c = -2;
Δ = b2-4ac
Δ = -1292-4·3·(-2)
Δ = 16665
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{-(-129)-\sqrt{16665}}{2*3}=\frac{129-\sqrt{16665}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+\sqrt{16665}}{2*3}=\frac{129+\sqrt{16665}}{6}
$