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1/2x+2/3x+5=5/2x+6
We move all terms to the left:
1/2x+2/3x+5-(5/2x+6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 2x+6)!=0We get rid of parentheses
x∈R
1/2x+2/3x-5/2x-6+5=0
We calculate fractions
(-15x+1)/6x^2+4x/6x^2-6+5=0
We add all the numbers together, and all the variables
(-15x+1)/6x^2+4x/6x^2-1=0
We multiply all the terms by the denominator
(-15x+1)+4x-1*6x^2=0
We add all the numbers together, and all the variables
4x+(-15x+1)-1*6x^2=0
Wy multiply elements
-6x^2+4x+(-15x+1)=0
We get rid of parentheses
-6x^2+4x-15x+1=0
We add all the numbers together, and all the variables
-6x^2-11x+1=0
a = -6; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·(-6)·1
Δ = 145
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{-(-11)-\sqrt{145}}{2*-6}=\frac{11-\sqrt{145}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*-6}=\frac{11+\sqrt{145}}{-12} $
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