a^2+6a-214=0

Solution for a^2+6a-214=0 equation:

a^2+6a-214=0

a = 1; b = 6; c = -214;
Δ = b2-4ac
Δ = 62-4·1·(-214)
Δ = 892
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{892}=\sqrt{4*223}=\sqrt{4}*\sqrt{223}=2\sqrt{223}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{223}}{2*1}=\frac{-6-2\sqrt{223}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{223}}{2*1}=\frac{-6+2\sqrt{223}}{2}
$