X=-2/3y+6

Solution for X=-2/3y+6 equation:

X=-2/3X+6

We move all terms to the left:

X-(-2/3X+6)=0


Domain of the equation: 3X+6)!=0

X∈R


We get rid of parentheses

X+2/3X-6=0

We multiply all the terms by the denominator


X*3X-6*3X+2=0

Wy multiply elements

3X^2-18X+2=0

a = 3; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·3·2
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-10\sqrt{3}}{2*3}=\frac{18-10\sqrt{3}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+10\sqrt{3}}{2*3}=\frac{18+10\sqrt{3}}{6}
$