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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2x(2x-1)

We multiply parentheses

4x^2-2x

Back to the equation:

-(4x^2-2x)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-4x^2+3x+2x+2=0

We add all the numbers together, and all the variables

-4x^2+5x+2=0

a = -4; b = 5; c = +2;
Δ = b2-4ac
Δ = 52-4·(-4)·2
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{57}}{2*-4}=\frac{-5-\sqrt{57}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{57}}{2*-4}=\frac{-5+\sqrt{57}}{-8}
$