6n^2-24=10n

Solution for 6n^2-24=10n equation:

6n^2-24=10n

We move all terms to the left:

6n^2-24-(10n)=0

a = 6; b = -10; c = -24;
Δ = b2-4ac
Δ = -102-4·6·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-26}{2*6}=\frac{-16}{12}
=-1+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+26}{2*6}=\frac{36}{12}
=3
$