(2x-3x^2)/(1-4x)=0

Solution for (2x-3x^2)/(1-4x)=0 equation:

(2x-3x^2)/(1-4x)=0


Domain of the equation: (1-4x)!=0

We move all terms containing x to the left, all other terms to the right

-4x!=-1

x!=-1/-4

x!=1/4

x∈R


We add all the numbers together, and all the variables

(2x-3x^2)/(-4x+1)=0

We multiply all the terms by the denominator


(2x-3x^2)=0

We get rid of parentheses

-3x^2+2x=0

a = -3; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-3)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-3}=\frac{-4}{-6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-3}=\frac{0}{-6}
=0
$