3a^2-1a-84=0

Solution for 3a^2-1a-84=0 equation:

3a^2-1a-84=0

a = 3; b = -1; c = -84;
Δ = b2-4ac
Δ = -12-4·3·(-84)
Δ = 1009
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{1009}}{2*3}=\frac{1-\sqrt{1009}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1009}}{2*3}=\frac{1+\sqrt{1009}}{6}
$