2a+3=1/2a+12

Solution for 2a+3=1/2a+12 equation:

2a+3=1/2a+12

We move all terms to the left:

2a+3-(1/2a+12)=0


Domain of the equation: 2a+12)!=0

a∈R


We get rid of parentheses

2a-1/2a-12+3=0

We multiply all the terms by the denominator


2a*2a-12*2a+3*2a-1=0

Wy multiply elements

4a^2-24a+6a-1=0

We add all the numbers together, and all the variables

4a^2-18a-1=0

a = 4; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·4·(-1)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{85}}{2*4}=\frac{18-2\sqrt{85}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{85}}{2*4}=\frac{18+2\sqrt{85}}{8}
$