3=2x(X-1)

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



3=2x(x-1)
We move all terms to the left:
3-(2x(x-1))=0
We calculate terms in parentheses: -(2x(x-1)), so:
2x(x-1)
We multiply parentheses
2x^2-2x
Back to the equation:
-(2x^2-2x)
We get rid of parentheses
-2x^2+2x+3=0
a = -2; b = 2; c = +3;
Δ = b2-4ac
Δ = 22-4·(-2)·3
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*-2}=\frac{-2-2\sqrt{7}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*-2}=\frac{-2+2\sqrt{7}}{-4} $

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