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X-1/5X=68
We move all terms to the left:
X-1/5X-(68)=0
Domain of the equation: 5X!=0We multiply all the terms by the denominator
X!=0/5
X!=0
X∈R
X*5X-68*5X-1=0
Wy multiply elements
5X^2-340X-1=0
a = 5; b = -340; c = -1;
Δ = b2-4ac
Δ = -3402-4·5·(-1)
Δ = 115620
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{115620}=\sqrt{4*28905}=\sqrt{4}*\sqrt{28905}=2\sqrt{28905}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-340)-2\sqrt{28905}}{2*5}=\frac{340-2\sqrt{28905}}{10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-340)+2\sqrt{28905}}{2*5}=\frac{340+2\sqrt{28905}}{10} $
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