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+14

Back to the equation:

-(-2a+14)


We get rid of parentheses

40a^2+8a+2a-14=0

We add all the numbers together, and all the variables

40a^2+10a-14=0

a = 40; b = 10; c = -14;
Δ = b2-4ac
Δ = 102-4·40·(-14)
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{65}}{2*40}=\frac{-10-6\sqrt{65}}{80}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{65}}{2*40}=\frac{-10+6\sqrt{65}}{80}
$