3n^2+6n-100=0

Solution for 3n^2+6n-100=0 equation:

3n^2+6n-100=0

a = 3; b = 6; c = -100;
Δ = b2-4ac
Δ = 62-4·3·(-100)
Δ = 1236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{309}}{2*3}=\frac{-6-2\sqrt{309}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{309}}{2*3}=\frac{-6+2\sqrt{309}}{6}
$