4.5a-3=1/2a+1

Solution for 4.5a-3=1/2a+1 equation:

4.5a-3=1/2a+1

We move all terms to the left:

4.5a-3-(1/2a+1)=0


Domain of the equation: 2a+1)!=0

a∈R


We get rid of parentheses

4.5a-1/2a-1-3=0

We multiply all the terms by the denominator


(4.5a)*2a-1*2a-3*2a-1=0

We add all the numbers together, and all the variables

(+4.5a)*2a-1*2a-3*2a-1=0

We multiply parentheses

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

Wy multiply elements

8a^2-2a-6a-1=0

We add all the numbers together, and all the variables

8a^2-8a-1=0

a = 8; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·8·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{6}}{2*8}=\frac{8-4\sqrt{6}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{6}}{2*8}=\frac{8+4\sqrt{6}}{16}
$