1/2a-a=14

Solution for 1/2a-a=14 equation:

1/2a-a=14

We move all terms to the left:

1/2a-a-(14)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+1/2a-14=0

We multiply all the terms by the denominator


-1a*2a-14*2a+1=0

Wy multiply elements

-2a^2-28a+1=0

a = -2; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·(-2)·1
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-6\sqrt{22}}{2*-2}=\frac{28-6\sqrt{22}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+6\sqrt{22}}{2*-2}=\frac{28+6\sqrt{22}}{-4}
$