3-x=2x(5x-1)

Solution for 3-x=2x(5x-1) equation:

3-x=2x(5x-1)

We move all terms to the left:

3-x-(2x(5x-1))=0

We add all the numbers together, and all the variables

-1x-(2x(5x-1))+3=0


We calculate terms in parentheses: -(2x(5x-1)), so:

2x(5x-1)

We multiply parentheses

10x^2-2x

Back to the equation:

-(10x^2-2x)


We get rid of parentheses

-10x^2-1x+2x+3=0

We add all the numbers together, and all the variables

-10x^2+x+3=0

a = -10; b = 1; c = +3;
Δ = b2-4ac
Δ = 12-4·(-10)·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*-10}=\frac{-12}{-20}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*-10}=\frac{10}{-20}
=-1/2
$