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5/5x=3-11/12x
We move all terms to the left:
5/5x-(3-11/12x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 12x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/5x-(-11/12x+3)=0
We get rid of parentheses
5/5x+11/12x-3=0
We calculate fractions
60x/60x^2+55x/60x^2-3=0
We multiply all the terms by the denominator
60x+55x-3*60x^2=0
We add all the numbers together, and all the variables
115x-3*60x^2=0
Wy multiply elements
-180x^2+115x=0
a = -180; b = 115; c = 0;
Δ = b2-4ac
Δ = 1152-4·(-180)·0
Δ = 13225
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{13225}=115$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-115}{2*-180}=\frac{-230}{-360} =23/36 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+115}{2*-180}=\frac{0}{-360} =0 $
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