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

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



5x(x+1)=-2x(x-2)
We move all terms to the left:
5x(x+1)-(-2x(x-2))=0
We multiply parentheses
5x^2+5x-(-2x(x-2))=0
We calculate terms in parentheses: -(-2x(x-2)), so:
-2x(x-2)
We multiply parentheses
-2x^2+4x
Back to the equation:
-(-2x^2+4x)
We get rid of parentheses
5x^2+2x^2-4x+5x=0
We add all the numbers together, and all the variables
7x^2+x=0
a = 7; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·7·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*7}=\frac{-2}{14} =-1/7 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*7}=\frac{0}{14} =0 $

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