3x+1/6x=10

Solution for 3x+1/6x=10 equation:

3x+1/6x=10

We move all terms to the left:

3x+1/6x-(10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


3x*6x-10*6x+1=0

Wy multiply elements

18x^2-60x+1=0

a = 18; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·18·1
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-42\sqrt{2}}{2*18}=\frac{60-42\sqrt{2}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+42\sqrt{2}}{2*18}=\frac{60+42\sqrt{2}}{36}
$