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12/x-8=2x
We move all terms to the left:
12/x-8-(2x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
-2x+12/x-8=0
We multiply all the terms by the denominator
-2x*x-8*x+12=0
We add all the numbers together, and all the variables
-8x-2x*x+12=0
Wy multiply elements
-2x^2-8x+12=0
a = -2; b = -8; c = +12;
Δ = b2-4ac
Δ = -82-4·(-2)·12
Δ = 160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*-2}=\frac{8-4\sqrt{10}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*-2}=\frac{8+4\sqrt{10}}{-4} $
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