X+1/4x=80

Solution for X+1/4x=80 equation:

X+1/4X=80

We move all terms to the left:

X+1/4X-(80)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-80*4X+1=0

Wy multiply elements

4X^2-320X+1=0

a = 4; b = -320; c = +1;
Δ = b2-4ac
Δ = -3202-4·4·1
Δ = 102384
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:

$\sqrt{\Delta}=\sqrt{102384}=\sqrt{1296*79}=\sqrt{1296}*\sqrt{79}=36\sqrt{79}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-36\sqrt{79}}{2*4}=\frac{320-36\sqrt{79}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+36\sqrt{79}}{2*4}=\frac{320+36\sqrt{79}}{8}
$