9-1/2a=4a+5

Solution for 9-1/2a=4a+5 equation:

9-1/2a=4a+5

We move all terms to the left:

9-1/2a-(4a+5)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We get rid of parentheses

-1/2a-4a-5+9=0

We multiply all the terms by the denominator


-4a*2a-5*2a+9*2a-1=0

Wy multiply elements

-8a^2-10a+18a-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 = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*-8}=\frac{-8-4\sqrt{2}}{-16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*-8}=\frac{-8+4\sqrt{2}}{-16}
$