-x(-x+11)=2+(4x+3)

Solution for -x(-x+11)=2+(4x+3) equation:

-x(-x+11)=2+(4x+3)

We move all terms to the left:

-x(-x+11)-(2+(4x+3))=0

We add all the numbers together, and all the variables

-x(-1x+11)-(2+(4x+3))=0

We multiply parentheses

1x^2-11x-(2+(4x+3))=0


We calculate terms in parentheses: -(2+(4x+3)), so:

2+(4x+3)

determiningTheFunctionDomain
(4x+3)+2

We get rid of parentheses

4x+3+2

We add all the numbers together, and all the variables

4x+5

Back to the equation:

-(4x+5)


We add all the numbers together, and all the variables

x^2-11x-(4x+5)=0

We get rid of parentheses

x^2-11x-4x-5=0

We add all the numbers together, and all the variables

x^2-15x-5=0

a = 1; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·1·(-5)
Δ = 245
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:

$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-7\sqrt{5}}{2*1}=\frac{15-7\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7\sqrt{5}}{2*1}=\frac{15+7\sqrt{5}}{2}
$