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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(x+6)-(x+29)=0

We multiply parentheses

x^2+6x-(x+29)=0

We get rid of parentheses

x^2+6x-x-29=0

We add all the numbers together, and all the variables

x^2+5x-29=0

a = 1; b = 5; c = -29;
Δ = b2-4ac
Δ = 52-4·1·(-29)
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{-(5)-\sqrt{141}}{2*1}=\frac{-5-\sqrt{141}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{141}}{2*1}=\frac{-5+\sqrt{141}}{2}
$