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3x-15/x=53
We move all terms to the left:
3x-15/x-(53)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
3x*x-53*x-15=0
We add all the numbers together, and all the variables
-53x+3x*x-15=0
Wy multiply elements
3x^2-53x-15=0
a = 3; b = -53; c = -15;
Δ = b2-4ac
Δ = -532-4·3·(-15)
Δ = 2989
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2989}=\sqrt{49*61}=\sqrt{49}*\sqrt{61}=7\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-7\sqrt{61}}{2*3}=\frac{53-7\sqrt{61}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+7\sqrt{61}}{2*3}=\frac{53+7\sqrt{61}}{6} $
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