Y=7x2-28x+14

Solution for Y=7x2-28x+14 equation:

=7Y^2-28Y+14

We move all terms to the left:

-(7Y^2-28Y+14)=0

We get rid of parentheses

-7Y^2+28Y-14=0

a = -7; b = 28; c = -14;
Δ = b2-4ac
Δ = 282-4·(-7)·(-14)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-14\sqrt{2}}{2*-7}=\frac{-28-14\sqrt{2}}{-14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+14\sqrt{2}}{2*-7}=\frac{-28+14\sqrt{2}}{-14}
$