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5/6x+12=1/4x-2
We move all terms to the left:
5/6x+12-(1/4x-2)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 4x-2)!=0We get rid of parentheses
x∈R
5/6x-1/4x+2+12=0
We calculate fractions
20x/24x^2+(-6x)/24x^2+2+12=0
We add all the numbers together, and all the variables
20x/24x^2+(-6x)/24x^2+14=0
We multiply all the terms by the denominator
20x+(-6x)+14*24x^2=0
Wy multiply elements
336x^2+20x+(-6x)=0
We get rid of parentheses
336x^2+20x-6x=0
We add all the numbers together, and all the variables
336x^2+14x=0
a = 336; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·336·0
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*336}=\frac{-28}{672} =-1/24 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*336}=\frac{0}{672} =0 $
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