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2/3x+5+3/4x-1/2+60=180
We move all terms to the left:
2/3x+5+3/4x-1/2+60-(180)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x!=0determiningTheFunctionDomain 2/3x+3/4x+5+60-180-1/2=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
2/3x+3/4x-115-1/2=0
We calculate fractions
(-48x^2)/48x^2+32x/48x^2+36x/48x^2-115=0
We multiply all the terms by the denominator
(-48x^2)+32x+36x-115*48x^2=0
We add all the numbers together, and all the variables
(-48x^2)+68x-115*48x^2=0
Wy multiply elements
(-48x^2)-5520x^2+68x=0
We get rid of parentheses
-48x^2-5520x^2+68x=0
We add all the numbers together, and all the variables
-5568x^2+68x=0
a = -5568; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-5568)·0
Δ = 4624
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{4624}=68$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-5568}=\frac{-136}{-11136} =17/1392 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-5568}=\frac{0}{-11136} =0 $
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