X+1/4x=4.5

Solution for X+1/4x=4.5 equation:

X+1/4X=4.5

We move all terms to the left:

X+1/4X-(4.5)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

X+1/4X-4.5=0

We multiply all the terms by the denominator


X*4X-(4.5)*4X+1=0

We multiply parentheses

X*4X-18X+1=0

Wy multiply elements

4X^2-18X+1=0

a = 4; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·4·1
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{77}}{2*4}=\frac{18-2\sqrt{77}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{77}}{2*4}=\frac{18+2\sqrt{77}}{8}
$