a2+9a-682=0

Solution for a2+9a-682=0 equation:

a2+9a-682=0

We add all the numbers together, and all the variables

a^2+9a-682=0

a = 1; b = 9; c = -682;
Δ = b2-4ac
Δ = 92-4·1·(-682)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-53}{2*1}=\frac{-62}{2}
=-31
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+53}{2*1}=\frac{44}{2}
=22
$