W^2-22=7-10w^2

Solution for W^2-22=7-10w^2 equation:

^2-22=7-10W^2

We move all terms to the left:

^2-22-(7-10W^2)=0

We add all the numbers together, and all the variables

-(7-10W^2)=0

We get rid of parentheses

10W^2-7=0

a = 10; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·10·(-7)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$W_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*10}=\frac{0-2\sqrt{70}}{20}
=-\frac{2\sqrt{70}}{20}
=-\frac{\sqrt{70}}{10}
$
$W_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*10}=\frac{0+2\sqrt{70}}{20}
=\frac{2\sqrt{70}}{20}
=\frac{\sqrt{70}}{10}
$