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

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

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

We move all terms to the left:

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

We multiply parentheses

-4a^2+2a+20a-10=0

We add all the numbers together, and all the variables

-4a^2+22a-10=0

a = -4; b = 22; c = -10;
Δ = b2-4ac
Δ = 222-4·(-4)·(-10)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-18}{2*-4}=\frac{-40}{-8}
=+5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+18}{2*-4}=\frac{-4}{-8}
=1/2
$