26n^2+7=16

Solution for 26n^2+7=16 equation:

26n^2+7=16

We move all terms to the left:

26n^2+7-(16)=0

We add all the numbers together, and all the variables

26n^2-9=0

a = 26; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·26·(-9)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{26}}{2*26}=\frac{0-6\sqrt{26}}{52}
=-\frac{6\sqrt{26}}{52}
=-\frac{3\sqrt{26}}{26}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{26}}{2*26}=\frac{0+6\sqrt{26}}{52}
=\frac{6\sqrt{26}}{52}
=\frac{3\sqrt{26}}{26}
$