-2/5x+1+5x=3

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Solution for -2/5x+1+5x=3 equation:



-2/5x+1+5x=3
We move all terms to the left:
-2/5x+1+5x-(3)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We add all the numbers together, and all the variables
5x-2/5x-2=0
We multiply all the terms by the denominator
5x*5x-2*5x-2=0
Wy multiply elements
25x^2-10x-2=0
a = 25; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·25·(-2)
Δ = 300
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:
$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{3}}{2*25}=\frac{10-10\sqrt{3}}{50} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{3}}{2*25}=\frac{10+10\sqrt{3}}{50} $

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