7n^2-15=32n

Solution for 7n^2-15=32n equation:

7n^2-15=32n

We move all terms to the left:

7n^2-15-(32n)=0

a = 7; b = -32; c = -15;
Δ = b2-4ac
Δ = -322-4·7·(-15)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-38}{2*7}=\frac{-6}{14}
=-3/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+38}{2*7}=\frac{70}{14}
=5
$