2a+4a(a-1)=1+3(2a+1)

Solution for 2a+4a(a-1)=1+3(2a+1) equation:

2a+4a(a-1)=1+3(2a+1)

We move all terms to the left:

2a+4a(a-1)-(1+3(2a+1))=0

We multiply parentheses

4a^2+2a-4a-(1+3(2a+1))=0


We calculate terms in parentheses: -(1+3(2a+1)), so:

1+3(2a+1)

determiningTheFunctionDomain
3(2a+1)+1

We multiply parentheses

6a+3+1

We add all the numbers together, and all the variables

6a+4

Back to the equation:

-(6a+4)


We add all the numbers together, and all the variables

4a^2-2a-(6a+4)=0

We get rid of parentheses

4a^2-2a-6a-4=0

We add all the numbers together, and all the variables

4a^2-8a-4=0

a = 4; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·4·(-4)
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{2}}{2*4}=\frac{8-8\sqrt{2}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{2}}{2*4}=\frac{8+8\sqrt{2}}{8}
$