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9/x-6=4x
We move all terms to the left:
9/x-6-(4x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
-4x+9/x-6=0
We multiply all the terms by the denominator
-4x*x-6*x+9=0
We add all the numbers together, and all the variables
-6x-4x*x+9=0
Wy multiply elements
-4x^2-6x+9=0
a = -4; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-4)·9
Δ = 180
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*-4}=\frac{6-6\sqrt{5}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*-4}=\frac{6+6\sqrt{5}}{-8} $
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