Y=1-7x^2

Solution for Y=1-7x^2 equation:

=1-7Y^2

We move all terms to the left:

-(1-7Y^2)=0

We get rid of parentheses

7Y^2-1=0

a = 7; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·7·(-1)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*7}=\frac{0-2\sqrt{7}}{14}
=-\frac{2\sqrt{7}}{14}
=-\frac{\sqrt{7}}{7}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*7}=\frac{0+2\sqrt{7}}{14}
=\frac{2\sqrt{7}}{14}
=\frac{\sqrt{7}}{7}
$