(X)=x^2-15x+54

Solution for (X)=x^2-15x+54 equation:

(X)=X^2-15X+54

We move all terms to the left:

(X)-(X^2-15X+54)=0

We get rid of parentheses

-X^2+X+15X-54=0

We add all the numbers together, and all the variables

-1X^2+16X-54=0

a = -1; b = 16; c = -54;
Δ = b2-4ac
Δ = 162-4·(-1)·(-54)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{10}}{2*-1}=\frac{-16-2\sqrt{10}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{10}}{2*-1}=\frac{-16+2\sqrt{10}}{-2}
$