(x+2)(3x+5)=2x(x+9)

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Solution for (x+2)(3x+5)=2x(x+9) equation:



(x+2)(3x+5)=2x(x+9)
We move all terms to the left:
(x+2)(3x+5)-(2x(x+9))=0
We multiply parentheses ..
(+3x^2+5x+6x+10)-(2x(x+9))=0
We calculate terms in parentheses: -(2x(x+9)), so:
2x(x+9)
We multiply parentheses
2x^2+18x
Back to the equation:
-(2x^2+18x)
We get rid of parentheses
3x^2-2x^2+5x+6x-18x+10=0
We add all the numbers together, and all the variables
x^2-7x+10=0
a = 1; b = -7; c = +10;
Δ = b2-4ac
Δ = -72-4·1·10
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*1}=\frac{4}{2} =2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*1}=\frac{10}{2} =5 $

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