13(x+1)=x(x+1)

Solution for 13(x+1)=x(x+1) equation:

13(x+1)=x(x+1)

We move all terms to the left:

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

We multiply parentheses

13x-(x(x+1))+13=0


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

x(x+1)

We multiply parentheses

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2+13x-x+13=0

We add all the numbers together, and all the variables

-1x^2+12x+13=0

a = -1; b = 12; c = +13;
Δ = b2-4ac
Δ = 122-4·(-1)·13
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-14}{2*-1}=\frac{-26}{-2}
=+13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+14}{2*-1}=\frac{2}{-2}
=-1
$