10x-8/3x=2

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Solution for 10x-8/3x=2 equation:



10x-8/3x=2
We move all terms to the left:
10x-8/3x-(2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We multiply all the terms by the denominator
10x*3x-2*3x-8=0
Wy multiply elements
30x^2-6x-8=0
a = 30; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·30·(-8)
Δ = 996
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:
$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{249}}{2*30}=\frac{6-2\sqrt{249}}{60} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{249}}{2*30}=\frac{6+2\sqrt{249}}{60} $

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