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

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



2(x+5)=x(2x+3)
We move all terms to the left:
2(x+5)-(x(2x+3))=0
We multiply parentheses
2x-(x(2x+3))+10=0
We calculate terms in parentheses: -(x(2x+3)), so:
x(2x+3)
We multiply parentheses
2x^2+3x
Back to the equation:
-(2x^2+3x)
We get rid of parentheses
-2x^2+2x-3x+10=0
We add all the numbers together, and all the variables
-2x^2-1x+10=0
a = -2; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-2)·10
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*-2}=\frac{-8}{-4} =+2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*-2}=\frac{10}{-4} =-2+1/2 $

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