2x-(4.5-1/2x)=-13

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Solution for 2x-(4.5-1/2x)=-13 equation: 



2x-(4.5-1/2x)=-13

We move all terms to the left:

2x-(4.5-1/2x)-(-13)=0



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

2x-(-1/2x+4.5)-(-13)=0

We add all the numbers together, and all the variables

2x-(-1/2x+4.5)+13=0

We get rid of parentheses

2x+1/2x-4.5+13=0

We multiply all the terms by the denominator


2x*2x-(4.5)*2x+13*2x+1=0

We multiply parentheses

2x*2x-9x+13*2x+1=0

Wy multiply elements

4x^2-9x+26x+1=0

We add all the numbers together, and all the variables

4x^2+17x+1=0

a = 4; b = 17; c = +1;
Δ = b2-4ac
Δ = 172-4·4·1
Δ = 273
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{-(17)-\sqrt{273}}{2*4}=\frac{-17-\sqrt{273}}{8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{273}}{2*4}=\frac{-17+\sqrt{273}}{8}
$

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