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5/3x+7=1/4x
We move all terms to the left:
5/3x+7-(1/4x)=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!=0/1
x!=0
x∈R
5/3x-(+1/4x)+7=0
We get rid of parentheses
5/3x-1/4x+7=0
We calculate fractions
20x/12x^2+(-3x)/12x^2+7=0
We multiply all the terms by the denominator
20x+(-3x)+7*12x^2=0
Wy multiply elements
84x^2+20x+(-3x)=0
We get rid of parentheses
84x^2+20x-3x=0
We add all the numbers together, and all the variables
84x^2+17x=0
a = 84; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·84·0
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*84}=\frac{-34}{168} =-17/84 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*84}=\frac{0}{168} =0 $
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