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2/3x-5/6=2-3/4x
We move all terms to the left:
2/3x-5/6-(2-3/4x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2/3x-(-3/4x+2)-5/6=0
We get rid of parentheses
2/3x+3/4x-2-5/6=0
We calculate fractions
(-240x^2)/432x^2+288x/432x^2+324x/432x^2-2=0
We multiply all the terms by the denominator
(-240x^2)+288x+324x-2*432x^2=0
We add all the numbers together, and all the variables
(-240x^2)+612x-2*432x^2=0
Wy multiply elements
(-240x^2)-864x^2+612x=0
We get rid of parentheses
-240x^2-864x^2+612x=0
We add all the numbers together, and all the variables
-1104x^2+612x=0
a = -1104; b = 612; c = 0;
Δ = b2-4ac
Δ = 6122-4·(-1104)·0
Δ = 374544
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{374544}=612$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(612)-612}{2*-1104}=\frac{-1224}{-2208} =51/92 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(612)+612}{2*-1104}=\frac{0}{-2208} =0 $
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