4a-4.5=14+3/2a-1

Solution for 4a-4.5=14+3/2a-1 equation:

4a-4.5=14+3/2a-1

We move all terms to the left:

4a-4.5-(14+3/2a-1)=0


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

a∈R


We add all the numbers together, and all the variables

4a-(3/2a+13)-4.5=0

We get rid of parentheses

4a-3/2a-13-4.5=0

We multiply all the terms by the denominator


4a*2a-13*2a-(4.5)*2a-3=0

We multiply parentheses

4a*2a-13*2a-9a-3=0

Wy multiply elements

8a^2-26a-9a-3=0

We add all the numbers together, and all the variables

8a^2-35a-3=0

a = 8; b = -35; c = -3;
Δ = b2-4ac
Δ = -352-4·8·(-3)
Δ = 1321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1321}}{2*8}=\frac{35-\sqrt{1321}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1321}}{2*8}=\frac{35+\sqrt{1321}}{16}
$