2n^2-2n=24

Solution for 2n^2-2n=24 equation:

2n^2-2n=24

We move all terms to the left:

2n^2-2n-(24)=0

a = 2; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·2·(-24)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*2}=\frac{-12}{4}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*2}=\frac{16}{4}
=4
$