(1/5)(20-4a)=6-a

Solution for (1/5)(20-4a)=6-a equation:

(1/5)(20-4a)=6-a

We move all terms to the left:

(1/5)(20-4a)-(6-a)=0


Domain of the equation: 5)(20-4a)!=0

a∈R


We add all the numbers together, and all the variables

(+1/5)(-4a+20)-(-1a+6)=0

We get rid of parentheses

(+1/5)(-4a+20)+1a-6=0

We multiply parentheses ..

(-4a^2+1/5*20)+1a-6=0

We multiply all the terms by the denominator


(-4a^2+1+1a*5*20)-6*5*20)=0

We add all the numbers together, and all the variables

(-4a^2+1+1a*5*20)=0

We get rid of parentheses

-4a^2+1a*5*20+1=0

Wy multiply elements

-4a^2+100a*2+1=0

Wy multiply elements

-4a^2+200a+1=0

a = -4; b = 200; c = +1;
Δ = b2-4ac
Δ = 2002-4·(-4)·1
Δ = 40016
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:

$\sqrt{\Delta}=\sqrt{40016}=\sqrt{16*2501}=\sqrt{16}*\sqrt{2501}=4\sqrt{2501}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2501}}{2*-4}=\frac{-200-4\sqrt{2501}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2501}}{2*-4}=\frac{-200+4\sqrt{2501}}{-8}
$