3n^2+16n+15=1

Solution for 3n^2+16n+15=1 equation:

3n^2+16n+15=1

We move all terms to the left:

3n^2+16n+15-(1)=0

We add all the numbers together, and all the variables

3n^2+16n+14=0

a = 3; b = 16; c = +14;
Δ = b2-4ac
Δ = 162-4·3·14
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{22}}{2*3}=\frac{-16-2\sqrt{22}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{22}}{2*3}=\frac{-16+2\sqrt{22}}{6}
$