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

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

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

We move all terms to the left:

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


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

2(x-1)x

We multiply parentheses

2x^2-2x

Back to the equation:

-(2x^2-2x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-2)·1
Δ = 17
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{-(3)-\sqrt{17}}{2*-2}=\frac{-3-\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{17}}{2*-2}=\frac{-3+\sqrt{17}}{-4}
$