x(x+1)=35+(x+x+1)

Solution for x(x+1)=35+(x+x+1) equation:

x(x+1)=35+(x+x+1)

We move all terms to the left:

x(x+1)-(35+(x+x+1))=0

We add all the numbers together, and all the variables

x(x+1)-(35+(2x+1))=0

We multiply parentheses

x^2+x-(35+(2x+1))=0


We calculate terms in parentheses: -(35+(2x+1)), so:

35+(2x+1)

determiningTheFunctionDomain
(2x+1)+35

We get rid of parentheses

2x+1+35

We add all the numbers together, and all the variables

2x+36

Back to the equation:

-(2x+36)


We get rid of parentheses

x^2+x-2x-36=0

We add all the numbers together, and all the variables

x^2-1x-36=0

a = 1; b = -1; c = -36;
Δ = b2-4ac
Δ = -12-4·1·(-36)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{145}}{2*1}=\frac{1-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*1}=\frac{1+\sqrt{145}}{2}
$