x+2/5x=210

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Solution for x+2/5x=210 equation: 



x+2/5x=210

We move all terms to the left:

x+2/5x-(210)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We multiply all the terms by the denominator


x*5x-210*5x+2=0

Wy multiply elements

5x^2-1050x+2=0

a = 5; b = -1050; c = +2;
Δ = b2-4ac
Δ = -10502-4·5·2
Δ = 1102460
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:


$\sqrt{\Delta}=\sqrt{1102460}=\sqrt{4*275615}=\sqrt{4}*\sqrt{275615}=2\sqrt{275615}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1050)-2\sqrt{275615}}{2*5}=\frac{1050-2\sqrt{275615}}{10}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1050)+2\sqrt{275615}}{2*5}=\frac{1050+2\sqrt{275615}}{10}
$

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