X(x+2)+(x+1)-(2x-1)=17

Solution for X(x+2)+(x+1)-(2x-1)=17 equation:

X(X+2)+(X+1)-(2X-1)=17

We move all terms to the left:

X(X+2)+(X+1)-(2X-1)-(17)=0

We multiply parentheses

X^2+2X+(X+1)-(2X-1)-17=0

We get rid of parentheses

X^2+2X+X-2X+1+1-17=0

We add all the numbers together, and all the variables

X^2+X-15=0

a = 1; b = 1; c = -15;
Δ = b2-4ac
Δ = 12-4·1·(-15)
Δ = 61
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{61}}{2*1}=\frac{-1-\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*1}=\frac{-1+\sqrt{61}}{2}
$