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

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

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

We move all terms to the left:

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

We multiply parentheses

5a^2-10a-(8(3a-4))=0


We calculate terms in parentheses: -(8(3a-4)), so:

8(3a-4)

We multiply parentheses

24a-32

Back to the equation:

-(24a-32)


We get rid of parentheses

5a^2-10a-24a+32=0

We add all the numbers together, and all the variables

5a^2-34a+32=0

a = 5; b = -34; c = +32;
Δ = b2-4ac
Δ = -342-4·5·32
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{129}}{2*5}=\frac{34-2\sqrt{129}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{129}}{2*5}=\frac{34+2\sqrt{129}}{10}
$