7n2+16n+15=2n2+3

Solution for 7n2+16n+15=2n2+3 equation:

7n^2+16n+15=2n^2+3

We move all terms to the left:

7n^2+16n+15-(2n^2+3)=0

We get rid of parentheses

7n^2-2n^2+16n-3+15=0

We add all the numbers together, and all the variables

5n^2+16n+12=0

a = 5; b = 16; c = +12;
Δ = b2-4ac
Δ = 162-4·5·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4}{2*5}=\frac{-20}{10}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4}{2*5}=\frac{-12}{10}
=-1+1/5
$