376=i^2*48

Solution for 376=i^2*48 equation:

376=i^2*48

We move all terms to the left:

376-(i^2*48)=0

We get rid of parentheses

-i^2*48+376=0

Wy multiply elements

-48i^2+376=0

a = -48; b = 0; c = +376;
Δ = b2-4ac
Δ = 02-4·(-48)·376
Δ = 72192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72192}=\sqrt{256*282}=\sqrt{256}*\sqrt{282}=16\sqrt{282}$
$i_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{282}}{2*-48}=\frac{0-16\sqrt{282}}{-96}
=-\frac{16\sqrt{282}}{-96}
=-\frac{\sqrt{282}}{-6}
$
$i_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{282}}{2*-48}=\frac{0+16\sqrt{282}}{-96}
=\frac{16\sqrt{282}}{-96}
=\frac{\sqrt{282}}{-6}
$