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1/5x-2/3+3/4x-4/5=5/3
We move all terms to the left:
1/5x-2/3+3/4x-4/5-(5/3)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
1/5x+3/4x-2/3-4/5-(+5/3)=0
We get rid of parentheses
1/5x+3/4x-2/3-4/5-5/3=0
We calculate fractions
(-2000x^2-2)/900x^2+36x/900x^2+675x/900x^2+(-144x)/900x^2=0
We multiply all the terms by the denominator
(-2000x^2-2)+36x+675x+(-144x)=0
We add all the numbers together, and all the variables
(-2000x^2-2)+711x+(-144x)=0
We get rid of parentheses
-2000x^2+711x-144x-2=0
We add all the numbers together, and all the variables
-2000x^2+567x-2=0
a = -2000; b = 567; c = -2;
Δ = b2-4ac
Δ = 5672-4·(-2000)·(-2)
Δ = 305489
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(567)-\sqrt{305489}}{2*-2000}=\frac{-567-\sqrt{305489}}{-4000} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(567)+\sqrt{305489}}{2*-2000}=\frac{-567+\sqrt{305489}}{-4000} $
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