X(x+2)=(x+4)+31

Solution for X(x+2)=(x+4)+31 equation:

X(X+2)=(X+4)+31

We move all terms to the left:

X(X+2)-((X+4)+31)=0

We multiply parentheses

X^2+2X-((X+4)+31)=0


We calculate terms in parentheses: -((X+4)+31), so:

(X+4)+31

We get rid of parentheses

X+4+31

We add all the numbers together, and all the variables

X+35

Back to the equation:

-(X+35)


We get rid of parentheses

X^2+2X-X-35=0

We add all the numbers together, and all the variables

X^2+X-35=0

a = 1; b = 1; c = -35;
Δ = b2-4ac
Δ = 12-4·1·(-35)
Δ = 141
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{141}}{2*1}=\frac{-1-\sqrt{141}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{141}}{2*1}=\frac{-1+\sqrt{141}}{2}
$