7-10w^2=1

Solution for 7-10w^2=1 equation:

7-10w^2=1

We move all terms to the left:

7-10w^2-(1)=0

We add all the numbers together, and all the variables

-10w^2+6=0

a = -10; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-10)·6
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*-10}=\frac{0-4\sqrt{15}}{-20}
=-\frac{4\sqrt{15}}{-20}
=-\frac{\sqrt{15}}{-5}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*-10}=\frac{0+4\sqrt{15}}{-20}
=\frac{4\sqrt{15}}{-20}
=\frac{\sqrt{15}}{-5}
$