2(2x-5)=-4x(x-1)

Solution for 2(2x-5)=-4x(x-1) equation:

2(2x-5)=-4x(x-1)

We move all terms to the left:

2(2x-5)-(-4x(x-1))=0

We multiply parentheses

4x-(-4x(x-1))-10=0


We calculate terms in parentheses: -(-4x(x-1)), so:

-4x(x-1)

We multiply parentheses

-4x^2+4x

Back to the equation:

-(-4x^2+4x)


We get rid of parentheses

4x^2-4x+4x-10=0

We add all the numbers together, and all the variables

4x^2-10=0

a = 4; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·4·(-10)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*4}=\frac{0-4\sqrt{10}}{8}
=-\frac{4\sqrt{10}}{8}
=-\frac{\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*4}=\frac{0+4\sqrt{10}}{8}
=\frac{4\sqrt{10}}{8}
=\frac{\sqrt{10}}{2}
$