a2-17a-84=0

Solution for a2-17a-84=0 equation:

a2-17a-84=0

We add all the numbers together, and all the variables

a^2-17a-84=0

a = 1; b = -17; c = -84;
Δ = b2-4ac
Δ = -172-4·1·(-84)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-25}{2*1}=\frac{-8}{2}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+25}{2*1}=\frac{42}{2}
=21
$