x(x+11)=(x+5)

Solution for x(x+11)=(x+5) equation:

x(x+11)=(x+5)

We move all terms to the left:

x(x+11)-((x+5))=0

We multiply parentheses

x^2+11x-((x+5))=0


We calculate terms in parentheses: -((x+5)), so:

(x+5)

We get rid of parentheses

x+5

Back to the equation:

-(x+5)


We get rid of parentheses

x^2+11x-x-5=0

We add all the numbers together, and all the variables

x^2+10x-5=0

a = 1; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·1·(-5)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{30}}{2*1}=\frac{-10-2\sqrt{30}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{30}}{2*1}=\frac{-10+2\sqrt{30}}{2}
$