x(x+1)=36-(x-1)

Solution for x(x+1)=36-(x-1) equation:

x(x+1)=36-(x-1)

We move all terms to the left:

x(x+1)-(36-(x-1))=0

We multiply parentheses

x^2+x-(36-(x-1))=0


We calculate terms in parentheses: -(36-(x-1)), so:

36-(x-1)

determiningTheFunctionDomain
-(x-1)+36

We get rid of parentheses

-x+1+36

We add all the numbers together, and all the variables

-1x+37

Back to the equation:

-(-1x+37)


We get rid of parentheses

x^2+x+1x-37=0

We add all the numbers together, and all the variables

x^2+2x-37=0

a = 1; b = 2; c = -37;
Δ = b2-4ac
Δ = 22-4·1·(-37)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{38}}{2*1}=\frac{-2-2\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{38}}{2*1}=\frac{-2+2\sqrt{38}}{2}
$