(1/2a)+3+a+3=44

Solution for (1/2a)+3+a+3=44 equation:

(1/2a)+3+a+3=44

We move all terms to the left:

(1/2a)+3+a+3-(44)=0


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

(+1/2a)+a+3+3-44=0

We add all the numbers together, and all the variables

a+(+1/2a)-38=0

We get rid of parentheses

a+1/2a-38=0

We multiply all the terms by the denominator


a*2a-38*2a+1=0

Wy multiply elements

2a^2-76a+1=0

a = 2; b = -76; c = +1;
Δ = b2-4ac
Δ = -762-4·2·1
Δ = 5768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5768}=\sqrt{4*1442}=\sqrt{4}*\sqrt{1442}=2\sqrt{1442}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{1442}}{2*2}=\frac{76-2\sqrt{1442}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{1442}}{2*2}=\frac{76+2\sqrt{1442}}{4}
$