a=(6a-(4a*4a))+(4+5a)

Solution for a=(6a-(4a*4a))+(4+5a) equation:

a=(6a-(4a*4a))+(4+5a)

We move all terms to the left:

a-((6a-(4a*4a))+(4+5a))=0

We add all the numbers together, and all the variables

a-((6a-(+4a*4a))+(5a+4))=0


We calculate terms in parentheses: -((6a-(+4a*4a))+(5a+4)), so:

(6a-(+4a*4a))+(5a+4)

We get rid of parentheses

(6a-(+4a*4a))+5a+4


We calculate terms in parentheses: +(6a-(+4a*4a)), so:

6a-(+4a*4a)

We get rid of parentheses

6a-4a*4a

Wy multiply elements

-16a^2+6a

Back to the equation:

+(-16a^2+6a)


We get rid of parentheses

-16a^2+6a+5a+4

We add all the numbers together, and all the variables

-16a^2+11a+4

Back to the equation:

-(-16a^2+11a+4)


We get rid of parentheses

16a^2-11a+a-4=0

We add all the numbers together, and all the variables

16a^2-10a-4=0

a = 16; b = -10; c = -4;
Δ = b2-4ac
Δ = -102-4·16·(-4)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{89}}{2*16}=\frac{10-2\sqrt{89}}{32}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{89}}{2*16}=\frac{10+2\sqrt{89}}{32}
$