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

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



5x(x-2)=2(x+1)
We move all terms to the left:
5x(x-2)-(2(x+1))=0
We multiply parentheses
5x^2-10x-(2(x+1))=0
We calculate terms in parentheses: -(2(x+1)), so:
2(x+1)
We multiply parentheses
2x+2
Back to the equation:
-(2x+2)
We get rid of parentheses
5x^2-10x-2x-2=0
We add all the numbers together, and all the variables
5x^2-12x-2=0
a = 5; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·5·(-2)
Δ = 184
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:
$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{46}}{2*5}=\frac{12-2\sqrt{46}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{46}}{2*5}=\frac{12+2\sqrt{46}}{10} $

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