(X+1)(9x-61)=x

Solution for (X+1)(9x-61)=x equation:

(X+1)(9X-61)=X

We move all terms to the left:

(X+1)(9X-61)-(X)=0

We add all the numbers together, and all the variables

-1X+(X+1)(9X-61)=0

We multiply parentheses ..

(+9X^2-61X+9X-61)-1X=0

We get rid of parentheses

9X^2-61X+9X-1X-61=0

We add all the numbers together, and all the variables

9X^2-53X-61=0

a = 9; b = -53; c = -61;
Δ = b2-4ac
Δ = -532-4·9·(-61)
Δ = 5005
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{-(-53)-\sqrt{5005}}{2*9}=\frac{53-\sqrt{5005}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{5005}}{2*9}=\frac{53+\sqrt{5005}}{18}
$