2(a-5)=4a(-2a-10)

Solution for 2(a-5)=4a(-2a-10) equation:

2(a-5)=4a(-2a-10)

We move all terms to the left:

2(a-5)-(4a(-2a-10))=0

We multiply parentheses

2a-(4a(-2a-10))-10=0


We calculate terms in parentheses: -(4a(-2a-10)), so:

4a(-2a-10)

We multiply parentheses

-8a^2-40a

Back to the equation:

-(-8a^2-40a)


We get rid of parentheses

8a^2+40a+2a-10=0

We add all the numbers together, and all the variables

8a^2+42a-10=0

a = 8; b = 42; c = -10;
Δ = b2-4ac
Δ = 422-4·8·(-10)
Δ = 2084
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:

$\sqrt{\Delta}=\sqrt{2084}=\sqrt{4*521}=\sqrt{4}*\sqrt{521}=2\sqrt{521}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{521}}{2*8}=\frac{-42-2\sqrt{521}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{521}}{2*8}=\frac{-42+2\sqrt{521}}{16}
$