x(x+2)-9=91+2x

Solution for x(x+2)-9=91+2x equation:

x(x+2)-9=91+2x

We move all terms to the left:

x(x+2)-9-(91+2x)=0

We add all the numbers together, and all the variables

x(x+2)-(2x+91)-9=0

We multiply parentheses

x^2+2x-(2x+91)-9=0

We get rid of parentheses

x^2+2x-2x-91-9=0

We add all the numbers together, and all the variables

x^2-100=0

a = 1; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·1·(-100)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20}{2*1}=\frac{20}{2}
=10
$