w^2+6=174

Solution for w^2+6=174 equation:

w^2+6=174

We move all terms to the left:

w^2+6-(174)=0

We add all the numbers together, and all the variables

w^2-168=0

a = 1; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·1·(-168)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*1}=\frac{0-4\sqrt{42}}{2}
=-\frac{4\sqrt{42}}{2}
=-2\sqrt{42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*1}=\frac{0+4\sqrt{42}}{2}
=\frac{4\sqrt{42}}{2}
=2\sqrt{42}
$