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x-3/5x=4
We move all terms to the left:
x-3/5x-(4)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
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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