7n^2-24=22n

Solution for 7n^2-24=22n equation:

7n^2-24=22n

We move all terms to the left:

7n^2-24-(22n)=0

a = 7; b = -22; c = -24;
Δ = b2-4ac
Δ = -222-4·7·(-24)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-34}{2*7}=\frac{-12}{14}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+34}{2*7}=\frac{56}{14}
=4
$