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

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

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

We move all terms to the left:

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


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

3x(x-2)

We multiply parentheses

3x^2-6x

Back to the equation:

-(3x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+9x+5=0

a = -3; b = 9; c = +5;
Δ = b2-4ac
Δ = 92-4·(-3)·5
Δ = 141
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{-(9)-\sqrt{141}}{2*-3}=\frac{-9-\sqrt{141}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{141}}{2*-3}=\frac{-9+\sqrt{141}}{-6}
$