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3/5x+2x-3=18
We move all terms to the left:
3/5x+2x-3-(18)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
2x+3/5x-21=0
We multiply all the terms by the denominator
2x*5x-21*5x+3=0
Wy multiply elements
10x^2-105x+3=0
a = 10; b = -105; c = +3;
Δ = b2-4ac
Δ = -1052-4·10·3
Δ = 10905
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{-(-105)-\sqrt{10905}}{2*10}=\frac{105-\sqrt{10905}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{10905}}{2*10}=\frac{105+\sqrt{10905}}{20} $
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