Y=-7x^2+14x+1

Solution for Y=-7x^2+14x+1 equation:

=-7Y^2+14Y+1

We move all terms to the left:

-(-7Y^2+14Y+1)=0

We get rid of parentheses

7Y^2-14Y-1=0

a = 7; b = -14; c = -1;
Δ = b2-4ac
Δ = -142-4·7·(-1)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{14}}{2*7}=\frac{14-4\sqrt{14}}{14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{14}}{2*7}=\frac{14+4\sqrt{14}}{14}
$