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4/5x+2/3=5/6x-4
We move all terms to the left:
4/5x+2/3-(5/6x-4)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 6x-4)!=0We get rid of parentheses
x∈R
4/5x-5/6x+4+2/3=0
We calculate fractions
360x^2/270x^2+216x/270x^2+(-225x)/270x^2+4=0
We multiply all the terms by the denominator
360x^2+216x+(-225x)+4*270x^2=0
Wy multiply elements
360x^2+1080x^2+216x+(-225x)=0
We get rid of parentheses
360x^2+1080x^2+216x-225x=0
We add all the numbers together, and all the variables
1440x^2-9x=0
a = 1440; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1440·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1440}=\frac{0}{2880} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1440}=\frac{18}{2880} =1/160 $
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