X=x^2-8x+15

Solution for X=x^2-8x+15 equation:

X=X^2-8X+15

We move all terms to the left:

X-(X^2-8X+15)=0

We get rid of parentheses

-X^2+X+8X-15=0

We add all the numbers together, and all the variables

-1X^2+9X-15=0

a = -1; b = 9; c = -15;
Δ = b2-4ac
Δ = 92-4·(-1)·(-15)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{21}}{2*-1}=\frac{-9-\sqrt{21}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{21}}{2*-1}=\frac{-9+\sqrt{21}}{-2}
$