4.5+x=9/4x

Solution for 4.5+x=9/4x equation:

4.5+x=9/4x

We move all terms to the left:

4.5+x-(9/4x)=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-(+9/4x)+4.5=0

We get rid of parentheses

x-9/4x+4.5=0

We multiply all the terms by the denominator


x*4x+(4.5)*4x-9=0

We multiply parentheses

x*4x+18x-9=0

Wy multiply elements

4x^2+18x-9=0

a = 4; b = 18; c = -9;
Δ = b2-4ac
Δ = 182-4·4·(-9)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{13}}{2*4}=\frac{-18-6\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{13}}{2*4}=\frac{-18+6\sqrt{13}}{8}
$