3x*2+4x=5/2x+9

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Solution for 3x*2+4x=5/2x+9 equation:



3x*2+4x=5/2x+9
We move all terms to the left:
3x*2+4x-(5/2x+9)=0
Domain of the equation: 2x+9)!=0
x∈R
We add all the numbers together, and all the variables
4x+3x*2-(5/2x+9)=0
Wy multiply elements
4x+6x-(5/2x+9)=0
We get rid of parentheses
4x+6x-5/2x-9=0
We multiply all the terms by the denominator
4x*2x+6x*2x-9*2x-5=0
Wy multiply elements
8x^2+12x^2-18x-5=0
We add all the numbers together, and all the variables
20x^2-18x-5=0
a = 20; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·20·(-5)
Δ = 724
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:
$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{181}}{2*20}=\frac{18-2\sqrt{181}}{40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{181}}{2*20}=\frac{18+2\sqrt{181}}{40} $

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