8a(-5a-1)=-8-2(a-3)

Solution for 8a(-5a-1)=-8-2(a-3) equation:

8a(-5a-1)=-8-2(a-3)

We move all terms to the left:

8a(-5a-1)-(-8-2(a-3))=0

We multiply parentheses

-40a^2-8a-(-8-2(a-3))=0


We calculate terms in parentheses: -(-8-2(a-3)), so:

-8-2(a-3)

determiningTheFunctionDomain
-2(a-3)-8

We multiply parentheses

-2a+6-8

We add all the numbers together, and all the variables

-2a-2

Back to the equation:

-(-2a-2)


We get rid of parentheses

-40a^2-8a+2a+2=0

We add all the numbers together, and all the variables

-40a^2-6a+2=0

a = -40; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-40)·2
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{-(-6)-2\sqrt{89}}{2*-40}=\frac{6-2\sqrt{89}}{-80}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*-40}=\frac{6+2\sqrt{89}}{-80}
$