1/6x+3x=76

Solution for 1/6x+3x=76 equation:

1/6x+3x=76

We move all terms to the left:

1/6x+3x-(76)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3x+1/6x-76=0

We multiply all the terms by the denominator


3x*6x-76*6x+1=0

Wy multiply elements

18x^2-456x+1=0

a = 18; b = -456; c = +1;
Δ = b2-4ac
Δ = -4562-4·18·1
Δ = 207864
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:

$\sqrt{\Delta}=\sqrt{207864}=\sqrt{36*5774}=\sqrt{36}*\sqrt{5774}=6\sqrt{5774}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-456)-6\sqrt{5774}}{2*18}=\frac{456-6\sqrt{5774}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-456)+6\sqrt{5774}}{2*18}=\frac{456+6\sqrt{5774}}{36}
$