Y=-2x^2+28x-26

Solution for Y=-2x^2+28x-26 equation:

=-2Y^2+28Y-26

We move all terms to the left:

-(-2Y^2+28Y-26)=0

We get rid of parentheses

2Y^2-28Y+26=0

a = 2; b = -28; c = +26;
Δ = b2-4ac
Δ = -282-4·2·26
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-24}{2*2}=\frac{4}{4}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+24}{2*2}=\frac{52}{4}
=13
$