Y=2x^2-28x+72

Solution for Y=2x^2-28x+72 equation:

=2Y^2-28Y+72

We move all terms to the left:

-(2Y^2-28Y+72)=0

We get rid of parentheses

-2Y^2+28Y-72=0

a = -2; b = 28; c = -72;
Δ = b2-4ac
Δ = 282-4·(-2)·(-72)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{13}}{2*-2}=\frac{-28-4\sqrt{13}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{13}}{2*-2}=\frac{-28+4\sqrt{13}}{-4}
$