Y=7x^2-2x-9

Solution for Y=7x^2-2x-9 equation:

=7Y^2-2Y-9

We move all terms to the left:

-(7Y^2-2Y-9)=0

We get rid of parentheses

-7Y^2+2Y+9=0

a = -7; b = 2; c = +9;
Δ = b2-4ac
Δ = 22-4·(-7)·9
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*-7}=\frac{-18}{-14}
=1+2/7
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*-7}=\frac{14}{-14}
=-1
$