3x^2-4x/6=20x

Solution for 3x^2-4x/6=20x equation:

3x^2-4x/6=20x

We move all terms to the left:

3x^2-4x/6-(20x)=0

We add all the numbers together, and all the variables

3x^2-20x-4x/6=0

We multiply all the terms by the denominator


3x^2*6-20x*6-4x=0

We add all the numbers together, and all the variables

3x^2*6-4x-20x*6=0

Wy multiply elements

18x^2-4x-120x=0

We add all the numbers together, and all the variables

18x^2-124x=0

a = 18; b = -124; c = 0;
Δ = b2-4ac
Δ = -1242-4·18·0
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-124}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+124}{2*18}=\frac{248}{36}
=6+8/9
$