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10x-3/x=2
We move all terms to the left:
10x-3/x-(2)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
10x*x-2*x-3=0
We add all the numbers together, and all the variables
-2x+10x*x-3=0
Wy multiply elements
10x^2-2x-3=0
a = 10; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·10·(-3)
Δ = 124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*10}=\frac{2-2\sqrt{31}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*10}=\frac{2+2\sqrt{31}}{20} $
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