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1/4x+1/9x+1/4=11/18
We move all terms to the left:
1/4x+1/9x+1/4-(11/18)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 9x!=0We add all the numbers together, and all the variables
x!=0/9
x!=0
x∈R
1/4x+1/9x+1/4-(+11/18)=0
We get rid of parentheses
1/4x+1/9x+1/4-11/18=0
We calculate fractions
(-14256x^2)/10368x^2+162x/10368x^2+1152x/10368x^2+162x/10368x^2=0
We multiply all the terms by the denominator
(-14256x^2)+162x+1152x+162x=0
We add all the numbers together, and all the variables
(-14256x^2)+1476x=0
We get rid of parentheses
-14256x^2+1476x=0
a = -14256; b = 1476; c = 0;
Δ = b2-4ac
Δ = 14762-4·(-14256)·0
Δ = 2178576
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{2178576}=1476$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1476)-1476}{2*-14256}=\frac{-2952}{-28512} =41/396 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1476)+1476}{2*-14256}=\frac{0}{-28512} =0 $
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