X=3+1/4x

Solution for X=3+1/4x equation:

X=3+1/4X

We move all terms to the left:

X-(3+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-(1/4X+3)=0

We get rid of parentheses

X-1/4X-3=0

We multiply all the terms by the denominator


X*4X-3*4X-1=0

Wy multiply elements

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}
$