3=x(2x+1)

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Solution for 3=x(2x+1) equation:



3=x(2x+1)
We move all terms to the left:
3-(x(2x+1))=0
We calculate terms in parentheses: -(x(2x+1)), so:
x(2x+1)
We multiply parentheses
2x^2+x
Back to the equation:
-(2x^2+x)
We get rid of parentheses
-2x^2-x+3=0
We add all the numbers together, and all the variables
-2x^2-1x+3=0
a = -2; b = -1; c = +3;
Δ = b2-4ac
Δ = -12-4·(-2)·3
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-2}=\frac{-4}{-4} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-2}=\frac{6}{-4} =-1+1/2 $

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