x+1/6x=76

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

x+1/6x=76

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-456x+1=0

a = 6; b = -456; c = +1;
Δ = b2-4ac
Δ = -4562-4·6·1
Δ = 207912
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:

$\sqrt{\Delta}=\sqrt{207912}=\sqrt{4*51978}=\sqrt{4}*\sqrt{51978}=2\sqrt{51978}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-456)-2\sqrt{51978}}{2*6}=\frac{456-2\sqrt{51978}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-456)+2\sqrt{51978}}{2*6}=\frac{456+2\sqrt{51978}}{12}
$