x(x+4)=5(x+2)+2

Solution for x(x+4)=5(x+2)+2 equation:

x(x+4)=5(x+2)+2

We move all terms to the left:

x(x+4)-(5(x+2)+2)=0

We multiply parentheses

x^2+4x-(5(x+2)+2)=0


We calculate terms in parentheses: -(5(x+2)+2), so:

5(x+2)+2

We multiply parentheses

5x+10+2

We add all the numbers together, and all the variables

5x+12

Back to the equation:

-(5x+12)


We get rid of parentheses

x^2+4x-5x-12=0

We add all the numbers together, and all the variables

x^2-1x-12=0

a = 1; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*1}=\frac{8}{2}
=4
$