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3x-8/5x=1
We move all terms to the left:
3x-8/5x-(1)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x-1*5x-8=0
Wy multiply elements
15x^2-5x-8=0
a = 15; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·15·(-8)
Δ = 505
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{505}}{2*15}=\frac{5-\sqrt{505}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{505}}{2*15}=\frac{5+\sqrt{505}}{30} $
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