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

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

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

We move all terms to the left:

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

We multiply parentheses

5x-(2x(x+3))+15=0


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

2x(x+3)

We multiply parentheses

2x^2+6x

Back to the equation:

-(2x^2+6x)


We get rid of parentheses

-2x^2+5x-6x+15=0

We add all the numbers together, and all the variables

-2x^2-1x+15=0

a = -2; b = -1; c = +15;
Δ = b2-4ac
Δ = -12-4·(-2)·15
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-2}=\frac{12}{-4}
=-3
$