Y=x2-10x+22

Solution for Y=x2-10x+22 equation:

=Y2-10Y+22

We move all terms to the left:

-(Y2-10Y+22)=0

We add all the numbers together, and all the variables

-(+Y^2-10Y+22)=0

We get rid of parentheses

-Y^2+10Y-22=0

We add all the numbers together, and all the variables

-1Y^2+10Y-22=0

a = -1; b = 10; c = -22;
Δ = b2-4ac
Δ = 102-4·(-1)·(-22)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{3}}{2*-1}=\frac{-10-2\sqrt{3}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{3}}{2*-1}=\frac{-10+2\sqrt{3}}{-2}
$