n*2n=148

Solution for n*2n=148 equation:

n*2n=148

We move all terms to the left:

n*2n-(148)=0

Wy multiply elements

2n^2-148=0

a = 2; b = 0; c = -148;
Δ = b2-4ac
Δ = 02-4·2·(-148)
Δ = 1184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{74}}{2*2}=\frac{0-4\sqrt{74}}{4}
=-\frac{4\sqrt{74}}{4}
=-\sqrt{74}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{74}}{2*2}=\frac{0+4\sqrt{74}}{4}
=\frac{4\sqrt{74}}{4}
=\sqrt{74}
$