2w^2-3=55

Solution for 2w^2-3=55 equation:

2w^2-3=55

We move all terms to the left:

2w^2-3-(55)=0

We add all the numbers together, and all the variables

2w^2-58=0

a = 2; b = 0; c = -58;
Δ = b2-4ac
Δ = 02-4·2·(-58)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{29}}{2*2}=\frac{0-4\sqrt{29}}{4}
=-\frac{4\sqrt{29}}{4}
=-\sqrt{29}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{29}}{2*2}=\frac{0+4\sqrt{29}}{4}
=\frac{4\sqrt{29}}{4}
=\sqrt{29}
$