(8-2a)(6-2a)=(a)

Solution for (8-2a)(6-2a)=(a) equation:

(8-2a)(6-2a)=(a)

We move all terms to the left:

(8-2a)(6-2a)-((a))=0

determiningTheFunctionDomain
(8-2a)(6-2a)-a=0

We add all the numbers together, and all the variables

(-2a+8)(-2a+6)-a=0

We add all the numbers together, and all the variables

-1a+(-2a+8)(-2a+6)=0

We multiply parentheses ..

(+4a^2-12a-16a+48)-1a=0

We get rid of parentheses

4a^2-12a-16a-1a+48=0

We add all the numbers together, and all the variables

4a^2-29a+48=0

a = 4; b = -29; c = +48;
Δ = b2-4ac
Δ = -292-4·4·48
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-\sqrt{73}}{2*4}=\frac{29-\sqrt{73}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{73}}{2*4}=\frac{29+\sqrt{73}}{8}
$