1x+1/2x=4.50

Solution for 1x+1/2x=4.50 equation:

1x+1/2x=4.50

We move all terms to the left:

1x+1/2x-(4.50)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

x+1/2x-4.5=0

We multiply all the terms by the denominator


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

We multiply parentheses

x*2x-9x+1=0

Wy multiply elements

2x^2-9x+1=0

a = 2; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·2·1
Δ = 73
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{-(-9)-\sqrt{73}}{2*2}=\frac{9-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{73}}{2*2}=\frac{9+\sqrt{73}}{4}
$