2.25x+1/2x=44

Solution for 2.25x+1/2x=44 equation:

2.25x+1/2x=44

We move all terms to the left:

2.25x+1/2x-(44)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


(2.25x)*2x-44*2x+1=0

We add all the numbers together, and all the variables

(+2.25x)*2x-44*2x+1=0

We multiply parentheses

4x^2-44*2x+1=0

Wy multiply elements

4x^2-88x+1=0

a = 4; b = -88; c = +1;
Δ = b2-4ac
Δ = -882-4·4·1
Δ = 7728
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:

$\sqrt{\Delta}=\sqrt{7728}=\sqrt{16*483}=\sqrt{16}*\sqrt{483}=4\sqrt{483}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-4\sqrt{483}}{2*4}=\frac{88-4\sqrt{483}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+4\sqrt{483}}{2*4}=\frac{88+4\sqrt{483}}{8}
$