X+1/3x+5=17

Solution for X+1/3x+5=17 equation:

X+1/3X+5=17

We move all terms to the left:

X+1/3X+5-(17)=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+1/3X-12=0

We multiply all the terms by the denominator


X*3X-12*3X+1=0

Wy multiply elements

3X^2-36X+1=0

a = 3; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·3·1
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{321}}{2*3}=\frac{36-2\sqrt{321}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{321}}{2*3}=\frac{36+2\sqrt{321}}{6}
$