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1/3x+5/6=3/4x-2
We move all terms to the left:
1/3x+5/6-(3/4x-2)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x-2)!=0We get rid of parentheses
x∈R
1/3x-3/4x+2+5/6=0
We calculate fractions
240x^2/432x^2+144x/432x^2+(-324x)/432x^2+2=0
We multiply all the terms by the denominator
240x^2+144x+(-324x)+2*432x^2=0
Wy multiply elements
240x^2+864x^2+144x+(-324x)=0
We get rid of parentheses
240x^2+864x^2+144x-324x=0
We add all the numbers together, and all the variables
1104x^2-180x=0
a = 1104; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·1104·0
Δ = 32400
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{32400}=180$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*1104}=\frac{0}{2208} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*1104}=\frac{360}{2208} =15/92 $
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