2a+(5/2)a-(1/2)a-9=17

Solution for 2a+(5/2)a-(1/2)a-9=17 equation:

2a+(5/2)a-(1/2)a-9=17

We move all terms to the left:

2a+(5/2)a-(1/2)a-9-(17)=0


Domain of the equation: 2)a!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2a+(+5/2)a-(+1/2)a-9-17=0

We add all the numbers together, and all the variables

2a+(+5/2)a-(+1/2)a-26=0

We multiply parentheses

5a^2-a^2+2a-26=0

We add all the numbers together, and all the variables

4a^2+2a-26=0

a = 4; b = 2; c = -26;
Δ = b2-4ac
Δ = 22-4·4·(-26)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{105}}{2*4}=\frac{-2-2\sqrt{105}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{105}}{2*4}=\frac{-2+2\sqrt{105}}{8}
$