Y=14x^2+4x-9

Solution for Y=14x^2+4x-9 equation:

=14Y^2+4Y-9

We move all terms to the left:

-(14Y^2+4Y-9)=0

We get rid of parentheses

-14Y^2-4Y+9=0

a = -14; b = -4; c = +9;
Δ = b2-4ac
Δ = -42-4·(-14)·9
Δ = 520
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:

$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{130}}{2*-14}=\frac{4-2\sqrt{130}}{-28}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{130}}{2*-14}=\frac{4+2\sqrt{130}}{-28}
$