5n^2+20n+6/5=0

Solution for 5n^2+20n+6/5=0 equation:

5n^2+20n+6/5=0

We multiply all the terms by the denominator


5n^2*5+20n*5+6=0

Wy multiply elements

25n^2+100n+6=0

a = 25; b = 100; c = +6;
Δ = b2-4ac
Δ = 1002-4·25·6
Δ = 9400
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:

$\sqrt{\Delta}=\sqrt{9400}=\sqrt{100*94}=\sqrt{100}*\sqrt{94}=10\sqrt{94}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{94}}{2*25}=\frac{-100-10\sqrt{94}}{50}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{94}}{2*25}=\frac{-100+10\sqrt{94}}{50}
$