7n^2+16n+15=2n^2+5

Solution for 7n^2+16n+15=2n^2+5 equation:

7n^2+16n+15=2n^2+5

We move all terms to the left:

7n^2+16n+15-(2n^2+5)=0

We get rid of parentheses

7n^2-2n^2+16n-5+15=0

We add all the numbers together, and all the variables

5n^2+16n+10=0

a = 5; b = 16; c = +10;
Δ = b2-4ac
Δ = 162-4·5·10
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{14}}{2*5}=\frac{-16-2\sqrt{14}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{14}}{2*5}=\frac{-16+2\sqrt{14}}{10}
$