3x*2x=6(20-6x)

Solution for 3x*2x=6(20-6x) equation:

3x*2x=6(20-6x)

We move all terms to the left:

3x*2x-(6(20-6x))=0

We add all the numbers together, and all the variables

3x*2x-(6(-6x+20))=0

Wy multiply elements

6x^2-(6(-6x+20))=0


We calculate terms in parentheses: -(6(-6x+20)), so:

6(-6x+20)

We multiply parentheses

-36x+120

Back to the equation:

-(-36x+120)


We get rid of parentheses

6x^2+36x-120=0

a = 6; b = 36; c = -120;
Δ = b2-4ac
Δ = 362-4·6·(-120)
Δ = 4176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{29}}{2*6}=\frac{-36-12\sqrt{29}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{29}}{2*6}=\frac{-36+12\sqrt{29}}{12}
$