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

Solution for 5(x+3)=2x(x+6) equation:

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

We move all terms to the left:

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

We multiply parentheses

5x-(2x(x+6))+15=0


We calculate terms in parentheses: -(2x(x+6)), so:

2x(x+6)

We multiply parentheses

2x^2+12x

Back to the equation:

-(2x^2+12x)


We get rid of parentheses

-2x^2+5x-12x+15=0

We add all the numbers together, and all the variables

-2x^2-7x+15=0

a = -2; b = -7; c = +15;
Δ = b2-4ac
Δ = -72-4·(-2)·15
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-2}=\frac{20}{-4}
=-5
$