(x+11)(x-2)=2(x-11)-10

Solution for (x+11)(x-2)=2(x-11)-10 equation:

(x+11)(x-2)=2(x-11)-10

We move all terms to the left:

(x+11)(x-2)-(2(x-11)-10)=0

We multiply parentheses ..

(+x^2-2x+11x-22)-(2(x-11)-10)=0


We calculate terms in parentheses: -(2(x-11)-10), so:

2(x-11)-10

We multiply parentheses

2x-22-10

We add all the numbers together, and all the variables

2x-32

Back to the equation:

-(2x-32)


We get rid of parentheses

x^2-2x+11x-2x-22+32=0

We add all the numbers together, and all the variables

x^2+7x+10=0

a = 1; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*1}=\frac{-4}{2}
=-2
$