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10x-45/x=5

We move all terms to the left:

10x-45/x-(5)=0

Domain of the equation: x!=0We multiply all the terms by the denominator

x∈R

10x*x-5*x-45=0

We add all the numbers together, and all the variables

-5x+10x*x-45=0

Wy multiply elements

10x^2-5x-45=0

a = 10; b = -5; c = -45;

Δ = b^{2}-4ac

Δ = -5^{2}-4·10·(-45)

Δ = 1825

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{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{73}}{2*10}=\frac{5-5\sqrt{73}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{73}}{2*10}=\frac{5+5\sqrt{73}}{20} $

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