15n=2n^2+7

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

15n=2n^2+7

We move all terms to the left:

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

We get rid of parentheses

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

a = -2; b = 15; c = -7;
Δ = b2-4ac
Δ = 152-4·(-2)·(-7)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-13}{2*-2}=\frac{-28}{-4}
=+7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+13}{2*-2}=\frac{-2}{-4}
=1/2
$