40x=-50x(x-2)

Solution for 40x=-50x(x-2) equation:

40x=-50x(x-2)

We move all terms to the left:

40x-(-50x(x-2))=0


We calculate terms in parentheses: -(-50x(x-2)), so:

-50x(x-2)

We multiply parentheses

-50x^2+100x

Back to the equation:

-(-50x^2+100x)


We get rid of parentheses

50x^2-100x+40x=0

We add all the numbers together, and all the variables

50x^2-60x=0

a = 50; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·50·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*50}=\frac{0}{100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*50}=\frac{120}{100}
=1+1/5
$