X-1=1/4x+2

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

X-1=1/4X+2

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

4X^2-12X-1=0

a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8}
$