(1/2)x+(1/3)x+(1/9)x=17

Solution for (1/2)x+(1/3)x+(1/9)x=17 equation:

(1/2)x+(1/3)x+(1/9)x=17

We move all terms to the left:

(1/2)x+(1/3)x+(1/9)x-(17)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)x+(+1/3)x+(+1/9)x-17=0

We multiply parentheses

x^2+x^2+x^2-17=0

We add all the numbers together, and all the variables

3x^2-17=0

a = 3; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·3·(-17)
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*3}=\frac{0-2\sqrt{51}}{6}
=-\frac{2\sqrt{51}}{6}
=-\frac{\sqrt{51}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*3}=\frac{0+2\sqrt{51}}{6}
=\frac{2\sqrt{51}}{6}
=\frac{\sqrt{51}}{3}
$