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

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

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

We move all terms to the left:

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

We multiply parentheses

15x-((x+6)(3x+2))+10=0

We multiply parentheses ..

-((+3x^2+2x+18x+12))+15x+10=0


We calculate terms in parentheses: -((+3x^2+2x+18x+12)), so:

(+3x^2+2x+18x+12)

We get rid of parentheses

3x^2+2x+18x+12

We add all the numbers together, and all the variables

3x^2+20x+12

Back to the equation:

-(3x^2+20x+12)


We add all the numbers together, and all the variables

15x-(3x^2+20x+12)+10=0

We get rid of parentheses

-3x^2+15x-20x-12+10=0

We add all the numbers together, and all the variables

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

a = -3; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·(-3)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*-3}=\frac{4}{-6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*-3}=\frac{6}{-6}
=-1
$