6x+1/3x-7=17

Solution for 6x+1/3x-7=17 equation:

6x+1/3x-7=17

We move all terms to the left:

6x+1/3x-7-(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

6x+1/3x-24=0

We multiply all the terms by the denominator


6x*3x-24*3x+1=0

Wy multiply elements

18x^2-72x+1=0

a = 18; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·18·1
Δ = 5112
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:

$\sqrt{\Delta}=\sqrt{5112}=\sqrt{36*142}=\sqrt{36}*\sqrt{142}=6\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{142}}{2*18}=\frac{72-6\sqrt{142}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{142}}{2*18}=\frac{72+6\sqrt{142}}{36}
$