2x(x-9)=3x(x+8)

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Solution for 2x(x-9)=3x(x+8) equation:



2x(x-9)=3x(x+8)
We move all terms to the left:
2x(x-9)-(3x(x+8))=0
We multiply parentheses
2x^2-18x-(3x(x+8))=0
We calculate terms in parentheses: -(3x(x+8)), so:
3x(x+8)
We multiply parentheses
3x^2+24x
Back to the equation:
-(3x^2+24x)
We get rid of parentheses
2x^2-3x^2-18x-24x=0
We add all the numbers together, and all the variables
-1x^2-42x=0
a = -1; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-1)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-1}=\frac{0}{-2} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-1}=\frac{84}{-2} =-42 $

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