2n^2+16n-69=-2n^2+1

Solution for 2n^2+16n-69=-2n^2+1 equation:

2n^2+16n-69=-2n^2+1

We move all terms to the left:

2n^2+16n-69-(-2n^2+1)=0

We get rid of parentheses

2n^2+2n^2+16n-1-69=0

We add all the numbers together, and all the variables

4n^2+16n-70=0

a = 4; b = 16; c = -70;
Δ = b2-4ac
Δ = 162-4·4·(-70)
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{86}}{2*4}=\frac{-16-4\sqrt{86}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{86}}{2*4}=\frac{-16+4\sqrt{86}}{8}
$