X-2=-1/4x+2

Solution for X-2=-1/4x+2 equation:

X-2=-1/4X+2

We move all terms to the left:

X-2-(-1/4X+2)=0


Domain of the equation: 4X+2)!=0

X∈R


We get rid of parentheses

X+1/4X-2-2=0

We multiply all the terms by the denominator


X*4X-2*4X-2*4X+1=0

Wy multiply elements

4X^2-8X-8X+1=0

We add all the numbers together, and all the variables

4X^2-16X+1=0

a = 4; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·4·1
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{15}}{2*4}=\frac{16-4\sqrt{15}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{15}}{2*4}=\frac{16+4\sqrt{15}}{8}
$