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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

-2x(x-4)

We multiply parentheses

-2x^2+8x

Back to the equation:

-(-2x^2+8x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-4x-10=0

a = 2; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·2·(-10)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*2}=\frac{4-4\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*2}=\frac{4+4\sqrt{6}}{4}
$