2Y=x2-6x+5

Solution for 2Y=x2-6x+5 equation:

2=Y2-6Y+5

We move all terms to the left:

2-(Y2-6Y+5)=0

We add all the numbers together, and all the variables

-(+Y^2-6Y+5)+2=0

We get rid of parentheses

-Y^2+6Y-5+2=0

We add all the numbers together, and all the variables

-1Y^2+6Y-3=0

a = -1; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·(-1)·(-3)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{6}}{2*-1}=\frac{-6-2\sqrt{6}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{6}}{2*-1}=\frac{-6+2\sqrt{6}}{-2}
$