2-5x=3x(2-x)

Solution for 2-5x=3x(2-x) equation:

2-5x=3x(2-x)

We move all terms to the left:

2-5x-(3x(2-x))=0

We add all the numbers together, and all the variables

-5x-(3x(-1x+2))+2=0


We calculate terms in parentheses: -(3x(-1x+2)), so:

3x(-1x+2)

We multiply parentheses

-3x^2+6x

Back to the equation:

-(-3x^2+6x)


We get rid of parentheses

3x^2-6x-5x+2=0

We add all the numbers together, and all the variables

3x^2-11x+2=0

a = 3; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·3·2
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{97}}{2*3}=\frac{11-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*3}=\frac{11+\sqrt{97}}{6}
$