(x-6)(x+9)-x=2(x+23)

Solution for (x-6)(x+9)-x=2(x+23) equation:

(x-6)(x+9)-x=2(x+23)

We move all terms to the left:

(x-6)(x+9)-x-(2(x+23))=0

We add all the numbers together, and all the variables

-1x+(x-6)(x+9)-(2(x+23))=0

We multiply parentheses ..

(+x^2+9x-6x-54)-1x-(2(x+23))=0


We calculate terms in parentheses: -(2(x+23)), so:

2(x+23)

We multiply parentheses

2x+46

Back to the equation:

-(2x+46)


We get rid of parentheses

x^2+9x-6x-1x-2x-54-46=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
$