48=2+w*w*2

Solution for 48=2+w*w*2 equation:

48=2+w*w*2

We move all terms to the left:

48-(2+w*w*2)=0

We add all the numbers together, and all the variables

-(w*w*2+2)+48=0

We get rid of parentheses

-w*w*2-2+48=0

We add all the numbers together, and all the variables

-w*w*2+46=0

Wy multiply elements

-2w^2*2+46=0

Wy multiply elements

-4w^2+46=0

a = -4; b = 0; c = +46;
Δ = b2-4ac
Δ = 02-4·(-4)·46
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*-4}=\frac{0-4\sqrt{46}}{-8}
=-\frac{4\sqrt{46}}{-8}
=-\frac{\sqrt{46}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*-4}=\frac{0+4\sqrt{46}}{-8}
=\frac{4\sqrt{46}}{-8}
=\frac{\sqrt{46}}{-2}
$