x(x-2)=x+88

Solution for x(x-2)=x+88 equation:

x(x-2)=x+88

We move all terms to the left:

x(x-2)-(x+88)=0

We multiply parentheses

x^2-2x-(x+88)=0

We get rid of parentheses

x^2-2x-x-88=0

We add all the numbers together, and all the variables

x^2-3x-88=0

a = 1; b = -3; c = -88;
Δ = b2-4ac
Δ = -32-4·1·(-88)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-19}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+19}{2*1}=\frac{22}{2}
=11
$