X+1/4x=65

Solution for X+1/4x=65 equation:

X+1/4X=65

We move all terms to the left:

X+1/4X-(65)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-65*4X+1=0

Wy multiply elements

4X^2-260X+1=0

a = 4; b = -260; c = +1;
Δ = b2-4ac
Δ = -2602-4·4·1
Δ = 67584
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:

$\sqrt{\Delta}=\sqrt{67584}=\sqrt{1024*66}=\sqrt{1024}*\sqrt{66}=32\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-32\sqrt{66}}{2*4}=\frac{260-32\sqrt{66}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+32\sqrt{66}}{2*4}=\frac{260+32\sqrt{66}}{8}
$