Y=x^2-12x+10

Solution for Y=x^2-12x+10 equation:

=Y^2-12Y+10

We move all terms to the left:

-(Y^2-12Y+10)=0

We get rid of parentheses

-Y^2+12Y-10=0

We add all the numbers together, and all the variables

-1Y^2+12Y-10=0

a = -1; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·(-1)·(-10)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{26}}{2*-1}=\frac{-12-2\sqrt{26}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{26}}{2*-1}=\frac{-12+2\sqrt{26}}{-2}
$