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9(x)=1/2x-39(x)=-4
We move all terms to the left:
9(x)-(1/2x-39(x))=0
Domain of the equation: 2x-39x)!=0We add all the numbers together, and all the variables
x∈R
9x-(-39x+1/2x)=0
We get rid of parentheses
9x+39x-1/2x=0
We multiply all the terms by the denominator
9x*2x+39x*2x-1=0
Wy multiply elements
18x^2+78x^2-1=0
We add all the numbers together, and all the variables
96x^2-1=0
a = 96; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·96·(-1)
Δ = 384
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{6}}{2*96}=\frac{0-8\sqrt{6}}{192} =-\frac{8\sqrt{6}}{192} =-\frac{\sqrt{6}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{6}}{2*96}=\frac{0+8\sqrt{6}}{192} =\frac{8\sqrt{6}}{192} =\frac{\sqrt{6}}{24} $
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