# 10x-45/x=5

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## Solution for 10x-45/x=5 equation:

10x-45/x=5
We move all terms to the left:
10x-45/x-(5)=0

Domain of the equation: x!=0
x∈R

We multiply all the terms by the denominator

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 = b2-4acΔ = -52-4·10·(-45)Δ = 1825The delta value is higher than zero, so the equation has two solutionsWe 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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