3n^2+8n-21=0

Solution for 3n^2+8n-21=0 equation:

3n^2+8n-21=0

a = 3; b = 8; c = -21;
Δ = b2-4ac
Δ = 82-4·3·(-21)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{79}}{2*3}=\frac{-8-2\sqrt{79}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{79}}{2*3}=\frac{-8+2\sqrt{79}}{6}
$