122=w(2)+35

Solution for 122=w(2)+35 equation:

122=w(2)+35

We move all terms to the left:

122-(w(2)+35)=0

We add all the numbers together, and all the variables

-(+w^2+35)+122=0

We get rid of parentheses

-w^2-35+122=0

We add all the numbers together, and all the variables

-1w^2+87=0

a = -1; b = 0; c = +87;
Δ = b2-4ac
Δ = 02-4·(-1)·87
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{87}}{2*-1}=\frac{0-2\sqrt{87}}{-2}
=-\frac{2\sqrt{87}}{-2}
=-\frac{\sqrt{87}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{87}}{2*-1}=\frac{0+2\sqrt{87}}{-2}
=\frac{2\sqrt{87}}{-2}
=\frac{\sqrt{87}}{-1}
$