8a-3=3+1/2a

Solution for 8a-3=3+1/2a equation:

8a-3=3+1/2a

We move all terms to the left:

8a-3-(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

8a-(1/2a+3)-3=0

We get rid of parentheses

8a-1/2a-3-3=0

We multiply all the terms by the denominator


8a*2a-3*2a-3*2a-1=0

Wy multiply elements

16a^2-6a-6a-1=0

We add all the numbers together, and all the variables

16a^2-12a-1=0

a = 16; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·16·(-1)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*16}=\frac{12-4\sqrt{13}}{32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*16}=\frac{12+4\sqrt{13}}{32}
$