35a+a2=16986

Solution for 35a+a2=16986 equation:

35a+a2=16986

We move all terms to the left:

35a+a2-(16986)=0

We add all the numbers together, and all the variables

a^2+35a-16986=0

a = 1; b = 35; c = -16986;
Δ = b2-4ac
Δ = 352-4·1·(-16986)
Δ = 69169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{69169}=263$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-263}{2*1}=\frac{-298}{2}
=-149
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+263}{2*1}=\frac{228}{2}
=114
$