84n^2=24-44n

Solution for 84n^2=24-44n equation:

84n^2=24-44n

We move all terms to the left:

84n^2-(24-44n)=0

We add all the numbers together, and all the variables

84n^2-(-44n+24)=0

We get rid of parentheses

84n^2+44n-24=0

a = 84; b = 44; c = -24;
Δ = b2-4ac
Δ = 442-4·84·(-24)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-100}{2*84}=\frac{-144}{168}
=-6/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+100}{2*84}=\frac{56}{168}
=1/3
$