4x=13.5+9/2x

Solution for 4x=13.5+9/2x equation:

4x=13.5+9/2x

We move all terms to the left:

4x-(13.5+9/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(9/2x+13.5)=0

We get rid of parentheses

4x-9/2x-13.5=0

We multiply all the terms by the denominator


4x*2x-(13.5)*2x-9=0

We multiply parentheses

4x*2x-27x-9=0

Wy multiply elements

8x^2-27x-9=0

a = 8; b = -27; c = -9;
Δ = b2-4ac
Δ = -272-4·8·(-9)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{113}}{2*8}=\frac{27-3\sqrt{113}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{113}}{2*8}=\frac{27+3\sqrt{113}}{16}
$