51=w2+17

Solution for 51=w2+17 equation:

51=w2+17

We move all terms to the left:

51-(w2+17)=0

We add all the numbers together, and all the variables

-(+w^2+17)+51=0

We get rid of parentheses

-w^2-17+51=0

We add all the numbers together, and all the variables

-1w^2+34=0

a = -1; b = 0; c = +34;
Δ = b2-4ac
Δ = 02-4·(-1)·34
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{34}}{2*-1}=\frac{0-2\sqrt{34}}{-2}
=-\frac{2\sqrt{34}}{-2}
=-\frac{\sqrt{34}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{34}}{2*-1}=\frac{0+2\sqrt{34}}{-2}
=\frac{2\sqrt{34}}{-2}
=\frac{\sqrt{34}}{-1}
$