8-2x=5x(x-2)

Solution for 8-2x=5x(x-2) equation:

8-2x=5x(x-2)

We move all terms to the left:

8-2x-(5x(x-2))=0


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

5x(x-2)

We multiply parentheses

5x^2-10x

Back to the equation:

-(5x^2-10x)


We get rid of parentheses

-5x^2-2x+10x+8=0

We add all the numbers together, and all the variables

-5x^2+8x+8=0

a = -5; b = 8; c = +8;
Δ = b2-4ac
Δ = 82-4·(-5)·8
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{14}}{2*-5}=\frac{-8-4\sqrt{14}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{14}}{2*-5}=\frac{-8+4\sqrt{14}}{-10}
$