X(1/3x)=-2x+6

Solution for X(1/3x)=-2x+6 equation:

X(1/3X)=-2X+6

We move all terms to the left:

X(1/3X)-(-2X+6)=0


Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X(+1/3X)-(-2X+6)=0

We multiply parentheses

X^2-(-2X+6)=0

We get rid of parentheses

X^2+2X-6=0

a = 1; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·1·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*1}=\frac{-2-2\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*1}=\frac{-2+2\sqrt{7}}{2}
$