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1/3x+100=5/4x-10
We move all terms to the left:
1/3x+100-(5/4x-10)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x-10)!=0We get rid of parentheses
x∈R
1/3x-5/4x+10+100=0
We calculate fractions
4x/12x^2+(-15x)/12x^2+10+100=0
We add all the numbers together, and all the variables
4x/12x^2+(-15x)/12x^2+110=0
We multiply all the terms by the denominator
4x+(-15x)+110*12x^2=0
Wy multiply elements
1320x^2+4x+(-15x)=0
We get rid of parentheses
1320x^2+4x-15x=0
We add all the numbers together, and all the variables
1320x^2-11x=0
a = 1320; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·1320·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*1320}=\frac{0}{2640} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*1320}=\frac{22}{2640} =1/120 $
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