2n^2+5n=2

Solution for 2n^2+5n=2 equation:

2n^2+5n=2

We move all terms to the left:

2n^2+5n-(2)=0

a = 2; b = 5; c = -2;
Δ = b2-4ac
Δ = 52-4·2·(-2)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{41}}{2*2}=\frac{-5-\sqrt{41}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*2}=\frac{-5+\sqrt{41}}{4}
$