-4.9a^2+a=-21

Solution for -4.9a^2+a=-21 equation:

-4.9a^2+a=-21

We move all terms to the left:

-4.9a^2+a-(-21)=0

We add all the numbers together, and all the variables

-4.9a^2+a+21=0

a = -4.9; b = 1; c = +21;
Δ = b2-4ac
Δ = 12-4·(-4.9)·21
Δ = 412.6
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{-(1)-\sqrt{412.6}}{2*-4.9}=\frac{-1-\sqrt{412.6}}{-9.8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{412.6}}{2*-4.9}=\frac{-1+\sqrt{412.6}}{-9.8}
$