5a(a-2)=8(3a-4a)

Solution for 5a(a-2)=8(3a-4a) equation:

5a(a-2)=8(3a-4a)

We move all terms to the left:

5a(a-2)-(8(3a-4a))=0

We add all the numbers together, and all the variables

5a(a-2)-(8(-1a))=0

We multiply parentheses

5a^2-10a-(8(-1a))=0


We calculate terms in parentheses: -(8(-1a)), so:

8(-1a)

We multiply parentheses

-8a

Back to the equation:

-(-8a)


We get rid of parentheses

5a^2-10a+8a=0

We add all the numbers together, and all the variables

5a^2-2a=0

a = 5; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·5·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*5}=\frac{0}{10}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*5}=\frac{4}{10}
=2/5
$