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1/8x+5/6x=115/48
We move all terms to the left:
1/8x+5/6x-(115/48)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
1/8x+5/6x-(+115/48)=0
We get rid of parentheses
1/8x+5/6x-115/48=0
We calculate fractions
(-33120x^2)/9216x^2+1152x/9216x^2+7680x/9216x^2=0
We multiply all the terms by the denominator
(-33120x^2)+1152x+7680x=0
We add all the numbers together, and all the variables
(-33120x^2)+8832x=0
We get rid of parentheses
-33120x^2+8832x=0
a = -33120; b = 8832; c = 0;
Δ = b2-4ac
Δ = 88322-4·(-33120)·0
Δ = 78004224
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{78004224}=8832$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8832)-8832}{2*-33120}=\frac{-17664}{-66240} =4/15 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8832)+8832}{2*-33120}=\frac{0}{-66240} =0 $
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