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2x-3/5x+1=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
2x*5x+1*5x-3=0
Wy multiply elements
10x^2+5x-3=0
a = 10; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·10·(-3)
Δ = 145
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{145}}{2*10}=\frac{-5-\sqrt{145}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*10}=\frac{-5+\sqrt{145}}{20} $
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