2x+5/6x=17

Solution for 2x+5/6x=17 equation:

2x+5/6x=17

We move all terms to the left:

2x+5/6x-(17)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


2x*6x-17*6x+5=0

Wy multiply elements

12x^2-102x+5=0

a = 12; b = -102; c = +5;
Δ = b2-4ac
Δ = -1022-4·12·5
Δ = 10164
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:

$\sqrt{\Delta}=\sqrt{10164}=\sqrt{484*21}=\sqrt{484}*\sqrt{21}=22\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-22\sqrt{21}}{2*12}=\frac{102-22\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+22\sqrt{21}}{2*12}=\frac{102+22\sqrt{21}}{24}
$