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5/6x+9=3/4x+10
We move all terms to the left:
5/6x+9-(3/4x+10)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 4x+10)!=0We get rid of parentheses
x∈R
5/6x-3/4x-10+9=0
We calculate fractions
20x/24x^2+(-18x)/24x^2-10+9=0
We add all the numbers together, and all the variables
20x/24x^2+(-18x)/24x^2-1=0
We multiply all the terms by the denominator
20x+(-18x)-1*24x^2=0
Wy multiply elements
-24x^2+20x+(-18x)=0
We get rid of parentheses
-24x^2+20x-18x=0
We add all the numbers together, and all the variables
-24x^2+2x=0
a = -24; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-24)·0
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-24}=\frac{-4}{-48} =1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-24}=\frac{0}{-48} =0 $
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