X-2/3y=-4

Solution for X-2/3y=-4 equation:

X-2/3X=-4

We move all terms to the left:

X-2/3X-(-4)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X-2/3X+4=0

We multiply all the terms by the denominator


X*3X+4*3X-2=0

Wy multiply elements

3X^2+12X-2=0

a = 3; b = 12; c = -2;
Δ = b2-4ac
Δ = 122-4·3·(-2)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*3}=\frac{-12-2\sqrt{42}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*3}=\frac{-12+2\sqrt{42}}{6}
$