Y=-2x^2+14x+3

Solution for Y=-2x^2+14x+3 equation:

=-2Y^2+14Y+3

We move all terms to the left:

-(-2Y^2+14Y+3)=0

We get rid of parentheses

2Y^2-14Y-3=0

a = 2; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·2·(-3)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{55}}{2*2}=\frac{14-2\sqrt{55}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{55}}{2*2}=\frac{14+2\sqrt{55}}{4}
$