(5x+12)=2x(3x+3)

Solution for (5x+12)=2x(3x+3) equation:

(5x+12)=2x(3x+3)

We move all terms to the left:

(5x+12)-(2x(3x+3))=0

We get rid of parentheses

5x-(2x(3x+3))+12=0


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

2x(3x+3)

We multiply parentheses

6x^2+6x

Back to the equation:

-(6x^2+6x)


We get rid of parentheses

-6x^2+5x-6x+12=0

We add all the numbers together, and all the variables

-6x^2-1x+12=0

a = -6; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-6)·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-17}{2*-6}=\frac{-16}{-12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+17}{2*-6}=\frac{18}{-12}
=-1+1/2
$