a-32+55a=a(2a-8)-a2+39

Solution for a-32+55a=a(2a-8)-a2+39 equation:

a-32+55a=a(2a-8)-a2+39

We move all terms to the left:

a-32+55a-(a(2a-8)-a2+39)=0

We add all the numbers together, and all the variables

56a-(a(2a-8)-a2+39)-32=0


We calculate terms in parentheses: -(a(2a-8)-a2+39), so:

a(2a-8)-a2+39

We add all the numbers together, and all the variables

-1a^2+a(2a-8)+39

We multiply parentheses

-1a^2+2a^2-8a+39

We add all the numbers together, and all the variables

a^2-8a+39

Back to the equation:

-(a^2-8a+39)


We get rid of parentheses

-a^2+56a+8a-39-32=0

We add all the numbers together, and all the variables

-1a^2+64a-71=0

a = -1; b = 64; c = -71;
Δ = b2-4ac
Δ = 642-4·(-1)·(-71)
Δ = 3812
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:

$\sqrt{\Delta}=\sqrt{3812}=\sqrt{4*953}=\sqrt{4}*\sqrt{953}=2\sqrt{953}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-2\sqrt{953}}{2*-1}=\frac{-64-2\sqrt{953}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+2\sqrt{953}}{2*-1}=\frac{-64+2\sqrt{953}}{-2}
$