5(x+2)-3x=2x(x+5)

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Solution for 5(x+2)-3x=2x(x+5) equation:



5(x+2)-3x=2x(x+5)
We move all terms to the left:
5(x+2)-3x-(2x(x+5))=0
We add all the numbers together, and all the variables
-3x+5(x+2)-(2x(x+5))=0
We multiply parentheses
-3x+5x-(2x(x+5))+10=0
We calculate terms in parentheses: -(2x(x+5)), so:
2x(x+5)
We multiply parentheses
2x^2+10x
Back to the equation:
-(2x^2+10x)
We add all the numbers together, and all the variables
2x-(2x^2+10x)+10=0
We get rid of parentheses
-2x^2+2x-10x+10=0
We add all the numbers together, and all the variables
-2x^2-8x+10=0
a = -2; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-2}=\frac{-4}{-4} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-2}=\frac{20}{-4} =-5 $

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