Y=7x^2-2x-1

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

=7Y^2-2Y-1

We move all terms to the left:

-(7Y^2-2Y-1)=0

We get rid of parentheses

-7Y^2+2Y+1=0

a = -7; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-7)·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{2}}{2*-7}=\frac{-2-4\sqrt{2}}{-14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{2}}{2*-7}=\frac{-2+4\sqrt{2}}{-14}
$