X+2/3y=23

Solution for X+2/3y=23 equation:

X+2/3X=23

We move all terms to the left:

X+2/3X-(23)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-23*3X+2=0

Wy multiply elements

3X^2-69X+2=0

a = 3; b = -69; c = +2;
Δ = b2-4ac
Δ = -692-4·3·2
Δ = 4737
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{-(-69)-\sqrt{4737}}{2*3}=\frac{69-\sqrt{4737}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+\sqrt{4737}}{2*3}=\frac{69+\sqrt{4737}}{6}
$