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3/(6-f)-4=3f-4

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Solution for 3/(6-f)-4=3f-4 equation:



3/(6-f)-4=3f-4
We move all terms to the left:
3/(6-f)-4-(3f-4)=0
Domain of the equation: (6-f)!=0
We move all terms containing f to the left, all other terms to the right
-f!=-6
f!=-6/-1
f!=+6
f∈R
We add all the numbers together, and all the variables
3/(-1f+6)-(3f-4)-4=0
We get rid of parentheses
3/(-1f+6)-3f+4-4=0
We multiply all the terms by the denominator
-3f*(-1f+6)+4*(-1f+6)-4*(-1f+6)+3=0
We multiply parentheses
3f^2-18f-4f+4f+24-24+3=0
We add all the numbers together, and all the variables
3f^2-18f+3=0
a = 3; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·3·3
Δ = 288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
f_{1}=\frac{-b-\sqrt{\Delta}}{2a}
f_{2}=\frac{-b+\sqrt{\Delta}}{2a}

The end solution:
\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}
f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12\sqrt{2}}{2*3}=\frac{18-12\sqrt{2}}{6}
f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12\sqrt{2}}{2*3}=\frac{18+12\sqrt{2}}{6}

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