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5/6x-22/5x=117/30
We move all terms to the left:
5/6x-22/5x-(117/30)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
5/6x-22/5x-(+117/30)=0
We get rid of parentheses
5/6x-22/5x-117/30=0
We calculate fractions
(-17550x^2)/2700x^2+2250x/2700x^2+(-11880x)/2700x^2=0
We multiply all the terms by the denominator
(-17550x^2)+2250x+(-11880x)=0
We get rid of parentheses
-17550x^2+2250x-11880x=0
We add all the numbers together, and all the variables
-17550x^2-9630x=0
a = -17550; b = -9630; c = 0;
Δ = b2-4ac
Δ = -96302-4·(-17550)·0
Δ = 92736900
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{92736900}=9630$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9630)-9630}{2*-17550}=\frac{0}{-35100} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9630)+9630}{2*-17550}=\frac{19260}{-35100} =-107/195 $
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