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5/3x+7/4x=41/60
We move all terms to the left:
5/3x+7/4x-(41/60)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
5/3x+7/4x-(+41/60)=0
We get rid of parentheses
5/3x+7/4x-41/60=0
We calculate fractions
(-1968x^2)/4320x^2+7200x/4320x^2+7560x/4320x^2=0
We multiply all the terms by the denominator
(-1968x^2)+7200x+7560x=0
We add all the numbers together, and all the variables
(-1968x^2)+14760x=0
We get rid of parentheses
-1968x^2+14760x=0
a = -1968; b = 14760; c = 0;
Δ = b2-4ac
Δ = 147602-4·(-1968)·0
Δ = 217857600
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{217857600}=14760$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14760)-14760}{2*-1968}=\frac{-29520}{-3936} =7+1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14760)+14760}{2*-1968}=\frac{0}{-3936} =0 $
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