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-3/5-8/15x+1/3x=-60
We move all terms to the left:
-3/5-8/15x+1/3x-(-60)=0
Domain of the equation: 15x!=0
x!=0/15
x!=0
x∈R
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
-8/15x+1/3x+60-3/5=0
We calculate fractions
(-405x^2)/1125x^2+(-600x)/1125x^2+375x/1125x^2+60=0
We multiply all the terms by the denominator
(-405x^2)+(-600x)+375x+60*1125x^2=0
We add all the numbers together, and all the variables
(-405x^2)+375x+(-600x)+60*1125x^2=0
Wy multiply elements
(-405x^2)+67500x^2+375x+(-600x)=0
We get rid of parentheses
-405x^2+67500x^2+375x-600x=0
We add all the numbers together, and all the variables
67095x^2-225x=0
a = 67095; b = -225; c = 0;
Δ = b2-4ac
Δ = -2252-4·67095·0
Δ = 50625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{50625}=225$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-225}{2*67095}=\frac{0}{134190} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+225}{2*67095}=\frac{450}{134190} =5/1491 $
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