x(53+x)-(53+x)=233

Solution for x(53+x)-(53+x)=233 equation:

x(53+x)-(53+x)=233

We move all terms to the left:

x(53+x)-(53+x)-(233)=0

We add all the numbers together, and all the variables

x(x+53)-(x+53)-233=0

We multiply parentheses

x^2+53x-(x+53)-233=0

We get rid of parentheses

x^2+53x-x-53-233=0

We add all the numbers together, and all the variables

x^2+52x-286=0

a = 1; b = 52; c = -286;
Δ = b2-4ac
Δ = 522-4·1·(-286)
Δ = 3848
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:

$\sqrt{\Delta}=\sqrt{3848}=\sqrt{4*962}=\sqrt{4}*\sqrt{962}=2\sqrt{962}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{962}}{2*1}=\frac{-52-2\sqrt{962}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{962}}{2*1}=\frac{-52+2\sqrt{962}}{2}
$