2n2=46n+48

Solution for 2n2=46n+48 equation:

2n^2=46n+48

We move all terms to the left:

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

We get rid of parentheses

2n^2-46n-48=0

a = 2; b = -46; c = -48;
Δ = b2-4ac
Δ = -462-4·2·(-48)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-50}{2*2}=\frac{-4}{4}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+50}{2*2}=\frac{96}{4}
=24
$