1/5x+5x=65

Solution for 1/5x+5x=65 equation:

1/5x+5x=65

We move all terms to the left:

1/5x+5x-(65)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/5x-65=0

We multiply all the terms by the denominator


5x*5x-65*5x+1=0

Wy multiply elements

25x^2-325x+1=0

a = 25; b = -325; c = +1;
Δ = b2-4ac
Δ = -3252-4·25·1
Δ = 105525
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:

$\sqrt{\Delta}=\sqrt{105525}=\sqrt{225*469}=\sqrt{225}*\sqrt{469}=15\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-325)-15\sqrt{469}}{2*25}=\frac{325-15\sqrt{469}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-325)+15\sqrt{469}}{2*25}=\frac{325+15\sqrt{469}}{50}
$