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3/5x-12+x=19
We move all terms to the left:
3/5x-12+x-(19)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
x+3/5x-31=0
We multiply all the terms by the denominator
x*5x-31*5x+3=0
Wy multiply elements
5x^2-155x+3=0
a = 5; b = -155; c = +3;
Δ = b2-4ac
Δ = -1552-4·5·3
Δ = 23965
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{-(-155)-\sqrt{23965}}{2*5}=\frac{155-\sqrt{23965}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-155)+\sqrt{23965}}{2*5}=\frac{155+\sqrt{23965}}{10} $
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