x(55-x)=756

Solution for x(55-x)=756 equation:

x(55-x)=756

We move all terms to the left:

x(55-x)-(756)=0

We add all the numbers together, and all the variables

x(-1x+55)-756=0

We multiply parentheses

-1x^2+55x-756=0

a = -1; b = 55; c = -756;
Δ = b2-4ac
Δ = 552-4·(-1)·(-756)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-1}{2*-1}=\frac{-56}{-2}
=+28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+1}{2*-1}=\frac{-54}{-2}
=+27
$