(x+6)(3x=2)

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

(x+6)(3x=2)

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

3x^2-2x+18x-12=0

We add all the numbers together, and all the variables

3x^2+16x-12=0

a = 3; b = 16; c = -12;
Δ = b2-4ac
Δ = 162-4·3·(-12)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*3}=\frac{4}{6}
=2/3
$