w(1/2)=31/2-1

Solution for w(1/2)=31/2-1 equation:

w(1/2)=31/2-1

We move all terms to the left:

w(1/2)-(31/2-1)=0

We add all the numbers together, and all the variables

w(+1/2)-(31/2-1)=0

We multiply parentheses

w^2-(31/2-1)=0

We get rid of parentheses

w^2+1-31/2=0

We multiply all the terms by the denominator


w^2*2-31+1*2=0

We add all the numbers together, and all the variables

w^2*2-29=0

Wy multiply elements

2w^2-29=0

a = 2; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·2·(-29)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{58}}{2*2}=\frac{0-2\sqrt{58}}{4}
=-\frac{2\sqrt{58}}{4}
=-\frac{\sqrt{58}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{58}}{2*2}=\frac{0+2\sqrt{58}}{4}
=\frac{2\sqrt{58}}{4}
=\frac{\sqrt{58}}{2}
$