x+1/6x=25

Solution for x+1/6x=25 equation:

x+1/6x=25

We move all terms to the left:

x+1/6x-(25)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-25*6x+1=0

Wy multiply elements

6x^2-150x+1=0

a = 6; b = -150; c = +1;
Δ = b2-4ac
Δ = -1502-4·6·1
Δ = 22476
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:

$\sqrt{\Delta}=\sqrt{22476}=\sqrt{4*5619}=\sqrt{4}*\sqrt{5619}=2\sqrt{5619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5619}}{2*6}=\frac{150-2\sqrt{5619}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5619}}{2*6}=\frac{150+2\sqrt{5619}}{12}
$