X-1/4x=20

Solution for X-1/4x=20 equation:

X-1/4X=20

We move all terms to the left:

X-1/4X-(20)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-20*4X-1=0

Wy multiply elements

4X^2-80X-1=0

a = 4; b = -80; c = -1;
Δ = b2-4ac
Δ = -802-4·4·(-1)
Δ = 6416
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:

$\sqrt{\Delta}=\sqrt{6416}=\sqrt{16*401}=\sqrt{16}*\sqrt{401}=4\sqrt{401}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{401}}{2*4}=\frac{80-4\sqrt{401}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{401}}{2*4}=\frac{80+4\sqrt{401}}{8}
$