(1/5)(24-5a)=4-a

Solution for (1/5)(24-5a)=4-a equation:

(1/5)(24-5a)=4-a

We move all terms to the left:

(1/5)(24-5a)-(4-a)=0


Domain of the equation: 5)(24-5a)!=0

a∈R


We add all the numbers together, and all the variables

(+1/5)(-5a+24)-(-1a+4)=0

We get rid of parentheses

(+1/5)(-5a+24)+1a-4=0

We multiply parentheses ..

(-5a^2+1/5*24)+1a-4=0

We multiply all the terms by the denominator


(-5a^2+1+1a*5*24)-4*5*24)=0

We add all the numbers together, and all the variables

(-5a^2+1+1a*5*24)=0

We get rid of parentheses

-5a^2+1a*5*24+1=0

Wy multiply elements

-5a^2+120a*2+1=0

Wy multiply elements

-5a^2+240a+1=0

a = -5; b = 240; c = +1;
Δ = b2-4ac
Δ = 2402-4·(-5)·1
Δ = 57620
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:

$\sqrt{\Delta}=\sqrt{57620}=\sqrt{4*14405}=\sqrt{4}*\sqrt{14405}=2\sqrt{14405}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-2\sqrt{14405}}{2*-5}=\frac{-240-2\sqrt{14405}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+2\sqrt{14405}}{2*-5}=\frac{-240+2\sqrt{14405}}{-10}
$