X+x(x+6)=(x+8)+21

Solution for X+x(x+6)=(x+8)+21 equation:

X+X(X+6)=(X+8)+21

We move all terms to the left:

X+X(X+6)-((X+8)+21)=0

We multiply parentheses

X^2+X+6X-((X+8)+21)=0


We calculate terms in parentheses: -((X+8)+21), so:

(X+8)+21

We get rid of parentheses

X+8+21

We add all the numbers together, and all the variables

X+29

Back to the equation:

-(X+29)


We add all the numbers together, and all the variables

X^2+7X-(X+29)=0

We get rid of parentheses

X^2+7X-X-29=0

We add all the numbers together, and all the variables

X^2+6X-29=0

a = 1; b = 6; c = -29;
Δ = b2-4ac
Δ = 62-4·1·(-29)
Δ = 152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{38}}{2*1}=\frac{-6-2\sqrt{38}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{38}}{2*1}=\frac{-6+2\sqrt{38}}{2}
$