X=1/4x-2

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

X=1/4X-2

We move all terms to the left:

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


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

X∈R


We get rid of parentheses

X-1/4X+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

4X^2+8X-1=0

a = 4; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·4·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{5}}{2*4}=\frac{-8-4\sqrt{5}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{5}}{2*4}=\frac{-8+4\sqrt{5}}{8}
$