(X-21)=1/4x

Solution for (X-21)=1/4x equation:

(X-21)=1/4X

We move all terms to the left:

(X-21)-(1/4X)=0


Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(X-21)-(+1/4X)=0

We get rid of parentheses

X-1/4X-21=0

We multiply all the terms by the denominator


X*4X-21*4X-1=0

Wy multiply elements

4X^2-84X-1=0

a = 4; b = -84; c = -1;
Δ = b2-4ac
Δ = -842-4·4·(-1)
Δ = 7072
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:

$\sqrt{\Delta}=\sqrt{7072}=\sqrt{16*442}=\sqrt{16}*\sqrt{442}=4\sqrt{442}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{442}}{2*4}=\frac{84-4\sqrt{442}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{442}}{2*4}=\frac{84+4\sqrt{442}}{8}
$