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

Solution for x(2x-3)=-1+3x(1-x) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

-1+3x(-1x+1)

determiningTheFunctionDomain
3x(-1x+1)-1

We multiply parentheses

-3x^2+3x-1

Back to the equation:

-(-3x^2+3x-1)


We get rid of parentheses

2x^2+3x^2-3x-3x+1=0

We add all the numbers together, and all the variables

5x^2-6x+1=0

a = 5; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·5·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*5}=\frac{2}{10}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*5}=\frac{10}{10}
=1
$