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(-4/9)f=-3
We move all terms to the left:
(-4/9)f-(-3)=0
Domain of the equation: 9)f!=0We add all the numbers together, and all the variables
f!=0/1
f!=0
f∈R
(-4/9)f+3=0
We multiply parentheses
-4f^2+3=0
a = -4; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-4)·3
Δ = 48
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}$$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-4}=\frac{0-4\sqrt{3}}{-8} =-\frac{4\sqrt{3}}{-8} =-\frac{\sqrt{3}}{-2} $$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-4}=\frac{0+4\sqrt{3}}{-8} =\frac{4\sqrt{3}}{-8} =\frac{\sqrt{3}}{-2} $
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