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5/6x-19=-2/8x-25
We move all terms to the left:
5/6x-19-(-2/8x-25)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 8x-25)!=0We get rid of parentheses
x∈R
5/6x+2/8x+25-19=0
We calculate fractions
40x/48x^2+12x/48x^2+25-19=0
We add all the numbers together, and all the variables
40x/48x^2+12x/48x^2+6=0
We multiply all the terms by the denominator
40x+12x+6*48x^2=0
We add all the numbers together, and all the variables
52x+6*48x^2=0
Wy multiply elements
288x^2+52x=0
a = 288; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·288·0
Δ = 2704
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{2704}=52$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*288}=\frac{-104}{576} =-13/72 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*288}=\frac{0}{576} =0 $
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