2n^2+10n+13=7

Solution for 2n^2+10n+13=7 equation:

2n^2+10n+13=7

We move all terms to the left:

2n^2+10n+13-(7)=0

We add all the numbers together, and all the variables

2n^2+10n+6=0

a = 2; b = 10; c = +6;
Δ = b2-4ac
Δ = 102-4·2·6
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*2}=\frac{-10-2\sqrt{13}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*2}=\frac{-10+2\sqrt{13}}{4}
$