x-3/5x=4

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Solution for x-3/5x=4 equation:



x-3/5x=4
We move all terms to the left:
x-3/5x-(4)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We multiply all the terms by the denominator
x*5x-4*5x-3=0
Wy multiply elements
5x^2-20x-3=0
a = 5; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·5·(-3)
Δ = 460
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:
$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{115}}{2*5}=\frac{20-2\sqrt{115}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{115}}{2*5}=\frac{20+2\sqrt{115}}{10} $

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