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x+1/5x=96
We move all terms to the left:
x+1/5x-(96)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
x*5x-96*5x+1=0
Wy multiply elements
5x^2-480x+1=0
a = 5; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·5·1
Δ = 230380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{230380}=\sqrt{4*57595}=\sqrt{4}*\sqrt{57595}=2\sqrt{57595}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-2\sqrt{57595}}{2*5}=\frac{480-2\sqrt{57595}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+2\sqrt{57595}}{2*5}=\frac{480+2\sqrt{57595}}{10} $
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