2n2+7n+2=51

Solution for 2n2+7n+2=51 equation:

2n^2+7n+2=51

We move all terms to the left:

2n^2+7n+2-(51)=0

We add all the numbers together, and all the variables

2n^2+7n-49=0

a = 2; b = 7; c = -49;
Δ = b2-4ac
Δ = 72-4·2·(-49)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-21}{2*2}=\frac{-28}{4}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+21}{2*2}=\frac{14}{4}
=3+1/2
$