48-46n=-5n^2

Solution for 48-46n=-5n^2 equation:

48-46n=-5n^2

We move all terms to the left:

48-46n-(-5n^2)=0

We get rid of parentheses

5n^2-46n+48=0

a = 5; b = -46; c = +48;
Δ = b2-4ac
Δ = -462-4·5·48
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{-(-46)-34}{2*5}=\frac{12}{10}
=1+1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+34}{2*5}=\frac{80}{10}
=8
$