2.5x+1/2x=13.5+4.5x

Solution for 2.5x+1/2x=13.5+4.5x equation:

2.5x+1/2x=13.5+4.5x

We move all terms to the left:

2.5x+1/2x-(13.5+4.5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2.5x+1/2x-(4.5x+13.5)=0

We get rid of parentheses

2.5x+1/2x-4.5x-13.5=0

We multiply all the terms by the denominator


(2.5x)*2x-(4.5x)*2x-(13.5)*2x+1=0

We add all the numbers together, and all the variables

(+2.5x)*2x-(+4.5x)*2x-(13.5)*2x+1=0

We multiply parentheses

4x^2-8x^2-27x+1=0

We add all the numbers together, and all the variables

-4x^2-27x+1=0

a = -4; b = -27; c = +1;
Δ = b2-4ac
Δ = -272-4·(-4)·1
Δ = 745
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{745}}{2*-4}=\frac{27-\sqrt{745}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{745}}{2*-4}=\frac{27+\sqrt{745}}{-8}
$