7(2n+3)14n+21=0

Solution for 7(2n+3)14n+21=0 equation:

7(2n+3)14n+21=0

We multiply parentheses

196n^2+294n+21=0

a = 196; b = 294; c = +21;
Δ = b2-4ac
Δ = 2942-4·196·21
Δ = 69972
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:

$\sqrt{\Delta}=\sqrt{69972}=\sqrt{196*357}=\sqrt{196}*\sqrt{357}=14\sqrt{357}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(294)-14\sqrt{357}}{2*196}=\frac{-294-14\sqrt{357}}{392}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(294)+14\sqrt{357}}{2*196}=\frac{-294+14\sqrt{357}}{392}
$