15x=x^2+54

Solution for 15x=x^2+54 equation:

15x=x^2+54

We move all terms to the left:

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

We get rid of parentheses

-x^2+15x-54=0

We add all the numbers together, and all the variables

-1x^2+15x-54=0

a = -1; b = 15; c = -54;
Δ = b2-4ac
Δ = 152-4·(-1)·(-54)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*-1}=\frac{-12}{-2}
=+6
$