(1/2)(20-4a)=6-a

Solution for (1/2)(20-4a)=6-a equation:

(1/2)(20-4a)=6-a

We move all terms to the left:

(1/2)(20-4a)-(6-a)=0


Domain of the equation: 2)(20-4a)!=0

a∈R


We add all the numbers together, and all the variables

(+1/2)(-4a+20)-(-1a+6)=0

We get rid of parentheses

(+1/2)(-4a+20)+1a-6=0

We multiply parentheses ..

(-4a^2+1/2*20)+1a-6=0

We multiply all the terms by the denominator


(-4a^2+1+1a*2*20)-6*2*20)=0

We add all the numbers together, and all the variables

(-4a^2+1+1a*2*20)=0

We get rid of parentheses

-4a^2+1a*2*20+1=0

Wy multiply elements

-4a^2+40a*2+1=0

Wy multiply elements

-4a^2+80a+1=0

a = -4; b = 80; c = +1;
Δ = b2-4ac
Δ = 802-4·(-4)·1
Δ = 6416
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:

$\sqrt{\Delta}=\sqrt{6416}=\sqrt{16*401}=\sqrt{16}*\sqrt{401}=4\sqrt{401}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-4\sqrt{401}}{2*-4}=\frac{-80-4\sqrt{401}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+4\sqrt{401}}{2*-4}=\frac{-80+4\sqrt{401}}{-8}
$