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

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

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

We move all terms to the left:

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

We multiply parentheses

2x-(3x(x-5))+6=0


We calculate terms in parentheses: -(3x(x-5)), so:

3x(x-5)

We multiply parentheses

3x^2-15x

Back to the equation:

-(3x^2-15x)


We get rid of parentheses

-3x^2+2x+15x+6=0

We add all the numbers together, and all the variables

-3x^2+17x+6=0

a = -3; b = 17; c = +6;
Δ = b2-4ac
Δ = 172-4·(-3)·6
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-19}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+19}{2*-3}=\frac{2}{-6}
=-1/3
$