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3/4x+4=5+1/6x
We move all terms to the left:
3/4x+4-(5+1/6x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 6x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/4x-(1/6x+5)+4=0
We get rid of parentheses
3/4x-1/6x-5+4=0
We calculate fractions
18x/24x^2+(-4x)/24x^2-5+4=0
We add all the numbers together, and all the variables
18x/24x^2+(-4x)/24x^2-1=0
We multiply all the terms by the denominator
18x+(-4x)-1*24x^2=0
Wy multiply elements
-24x^2+18x+(-4x)=0
We get rid of parentheses
-24x^2+18x-4x=0
We add all the numbers together, and all the variables
-24x^2+14x=0
a = -24; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-24)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-24}=\frac{-28}{-48} =7/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-24}=\frac{0}{-48} =0 $
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