X(x+2)=3(x+1)+17

Solution for X(x+2)=3(x+1)+17 equation:

X(X+2)=3(X+1)+17

We move all terms to the left:

X(X+2)-(3(X+1)+17)=0

We multiply parentheses

X^2+2X-(3(X+1)+17)=0


We calculate terms in parentheses: -(3(X+1)+17), so:

3(X+1)+17

We multiply parentheses

3X+3+17

We add all the numbers together, and all the variables

3X+20

Back to the equation:

-(3X+20)


We get rid of parentheses

X^2+2X-3X-20=0

We add all the numbers together, and all the variables

X^2-1X-20=0

a = 1; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*1}=\frac{10}{2}
=5
$