9,5a-a^2=19,5

Solution for 9,5a-a^2=19,5 equation:

9.5a-a^2=19.5

We move all terms to the left:

9.5a-a^2-(19.5)=0

We add all the numbers together, and all the variables

-1a^2+9.5a-19.5=0

a = -1; b = 9.5; c = -19.5;
Δ = b2-4ac
Δ = 9.52-4·(-1)·(-19.5)
Δ = 12.25
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{-(9.5)-\sqrt{12.25}}{2*-1}=\frac{-9.5-\sqrt{12.25}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.5)+\sqrt{12.25}}{2*-1}=\frac{-9.5+\sqrt{12.25}}{-2}
$