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

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

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

We move all terms to the left:

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


Domain of the equation: 2)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

a^2+a-38=0

a = 1; b = 1; c = -38;
Δ = b2-4ac
Δ = 12-4·1·(-38)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{17}}{2*1}=\frac{-1-3\sqrt{17}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{17}}{2*1}=\frac{-1+3\sqrt{17}}{2}
$