-2n^2+2n+53=7

Solution for -2n^2+2n+53=7 equation:

-2n^2+2n+53=7

We move all terms to the left:

-2n^2+2n+53-(7)=0

We add all the numbers together, and all the variables

-2n^2+2n+46=0

a = -2; b = 2; c = +46;
Δ = b2-4ac
Δ = 22-4·(-2)·46
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{93}}{2*-2}=\frac{-2-2\sqrt{93}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{93}}{2*-2}=\frac{-2+2\sqrt{93}}{-4}
$