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

Solution for 3x(x-1)=5+2x(x-2) equation:

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

We move all terms to the left:

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

We multiply parentheses

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


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

5+2x(x-2)

determiningTheFunctionDomain
2x(x-2)+5

We multiply parentheses

2x^2-4x+5

Back to the equation:

-(2x^2-4x+5)


We get rid of parentheses

3x^2-2x^2-3x+4x-5=0

We add all the numbers together, and all the variables

x^2+x-5=0

a = 1; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·1·(-5)
Δ = 21
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{-(1)-\sqrt{21}}{2*1}=\frac{-1-\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*1}=\frac{-1+\sqrt{21}}{2}
$