6x=3x(3x+16)

Solution for 6x=3x(3x+16) equation:

6x=3x(3x+16)

We move all terms to the left:

6x-(3x(3x+16))=0


We calculate terms in parentheses: -(3x(3x+16)), so:

3x(3x+16)

We multiply parentheses

9x^2+48x

Back to the equation:

-(9x^2+48x)


We get rid of parentheses

-9x^2+6x-48x=0

We add all the numbers together, and all the variables

-9x^2-42x=0

a = -9; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-9)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-9}=\frac{84}{-18}
=-4+2/3
$