4a(1+a)-(4a*4a)-a=5(a-9)

Solution for 4a(1+a)-(4a*4a)-a=5(a-9) equation:

4a(1+a)-(4a*4a)-a=5(a-9)

We move all terms to the left:

4a(1+a)-(4a*4a)-a-(5(a-9))=0

We add all the numbers together, and all the variables

4a(a+1)-(+4a*4a)-a-(5(a-9))=0

We add all the numbers together, and all the variables

-1a+4a(a+1)-(+4a*4a)-(5(a-9))=0

We multiply parentheses

4a^2-1a+4a-(+4a*4a)-(5(a-9))=0

We get rid of parentheses

4a^2-1a+4a-4a*4a-(5(a-9))=0


We calculate terms in parentheses: -(5(a-9)), so:

5(a-9)

We multiply parentheses

5a-45

Back to the equation:

-(5a-45)


We add all the numbers together, and all the variables

4a^2+3a-4a*4a-(5a-45)=0

Wy multiply elements

4a^2-16a^2+3a-(5a-45)=0

We get rid of parentheses

4a^2-16a^2+3a-5a+45=0

We add all the numbers together, and all the variables

-12a^2-2a+45=0

a = -12; b = -2; c = +45;
Δ = b2-4ac
Δ = -22-4·(-12)·45
Δ = 2164
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:

$\sqrt{\Delta}=\sqrt{2164}=\sqrt{4*541}=\sqrt{4}*\sqrt{541}=2\sqrt{541}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{541}}{2*-12}=\frac{2-2\sqrt{541}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{541}}{2*-12}=\frac{2+2\sqrt{541}}{-24}
$