2a+3=1/2a

Solution for 2a+3=1/2a equation:

2a+3=1/2a

We move all terms to the left:

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


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2a-1/2a+3=0

We multiply all the terms by the denominator


2a*2a+3*2a-1=0

Wy multiply elements

4a^2+6a-1=0

a = 4; b = 6; c = -1;
Δ = b2-4ac
Δ = 62-4·4·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{13}}{2*4}=\frac{-6-2\sqrt{13}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*4}=\frac{-6+2\sqrt{13}}{8}
$