X=-2/3y+3

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

X=-2/3X+3

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

X+2/3X-3=0

We multiply all the terms by the denominator


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

Wy multiply elements

3X^2-9X+2=0

a = 3; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·3·2
Δ = 57
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{-(-9)-\sqrt{57}}{2*3}=\frac{9-\sqrt{57}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*3}=\frac{9+\sqrt{57}}{6}
$