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1/3x+1/4x=25
We move all terms to the left:
1/3x+1/4x-(25)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 4x!=0We calculate fractions
x!=0/4
x!=0
x∈R
4x/12x^2+3x/12x^2-25=0
We multiply all the terms by the denominator
4x+3x-25*12x^2=0
We add all the numbers together, and all the variables
7x-25*12x^2=0
Wy multiply elements
-300x^2+7x=0
a = -300; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-300)·0
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-300}=\frac{-14}{-600} =7/300 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-300}=\frac{0}{-600} =0 $
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