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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(5a-2)), so:

2(5a-2)

We multiply parentheses

10a-4

Back to the equation:

-(10a-4)


We get rid of parentheses

4a^2-8a-10a+4=0

We add all the numbers together, and all the variables

4a^2-18a+4=0

a = 4; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·4·4
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{65}}{2*4}=\frac{18-2\sqrt{65}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{65}}{2*4}=\frac{18+2\sqrt{65}}{8}
$