X+8/3y=12

Solution for X+8/3y=12 equation:

X+8/3X=12

We move all terms to the left:

X+8/3X-(12)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-12*3X+8=0

Wy multiply elements

3X^2-36X+8=0

a = 3; b = -36; c = +8;
Δ = b2-4ac
Δ = -362-4·3·8
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-20\sqrt{3}}{2*3}=\frac{36-20\sqrt{3}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+20\sqrt{3}}{2*3}=\frac{36+20\sqrt{3}}{6}
$