5a(a+2)=a(6+2a)+10a

Solution for 5a(a+2)=a(6+2a)+10a equation:

5a(a+2)=a(6+2a)+10a

We move all terms to the left:

5a(a+2)-(a(6+2a)+10a)=0

We add all the numbers together, and all the variables

5a(a+2)-(a(2a+6)+10a)=0

We multiply parentheses

5a^2+10a-(a(2a+6)+10a)=0


We calculate terms in parentheses: -(a(2a+6)+10a), so:

a(2a+6)+10a

We add all the numbers together, and all the variables

10a+a(2a+6)

We multiply parentheses

2a^2+10a+6a

We add all the numbers together, and all the variables

2a^2+16a

Back to the equation:

-(2a^2+16a)


We get rid of parentheses

5a^2-2a^2+10a-16a=0

We add all the numbers together, and all the variables

3a^2-6a=0

a = 3; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·3·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*3}=\frac{0}{6}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*3}=\frac{12}{6}
=2
$