2n^2+20n=30

Solution for 2n^2+20n=30 equation:

2n^2+20n=30

We move all terms to the left:

2n^2+20n-(30)=0

a = 2; b = 20; c = -30;
Δ = b2-4ac
Δ = 202-4·2·(-30)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{10}}{2*2}=\frac{-20-8\sqrt{10}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{10}}{2*2}=\frac{-20+8\sqrt{10}}{4}
$