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3x+9=1/2x
We move all terms to the left:
3x+9-(1/2x)=0
Domain of the equation: 2x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3x-(+1/2x)+9=0
We get rid of parentheses
3x-1/2x+9=0
We multiply all the terms by the denominator
3x*2x+9*2x-1=0
Wy multiply elements
6x^2+18x-1=0
a = 6; b = 18; c = -1;
Δ = b2-4ac
Δ = 182-4·6·(-1)
Δ = 348
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{87}}{2*6}=\frac{-18-2\sqrt{87}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{87}}{2*6}=\frac{-18+2\sqrt{87}}{12} $
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