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6/b-1/2b=5
We move all terms to the left:
6/b-1/2b-(5)=0
Domain of the equation: b!=0
b∈R
Domain of the equation: 2b!=0We calculate fractions
b!=0/2
b!=0
b∈R
12b/2b^2+(-b)/2b^2-5=0
We add all the numbers together, and all the variables
12b/2b^2+(-1b)/2b^2-5=0
We multiply all the terms by the denominator
12b+(-1b)-5*2b^2=0
Wy multiply elements
-10b^2+12b+(-1b)=0
We get rid of parentheses
-10b^2+12b-1b=0
We add all the numbers together, and all the variables
-10b^2+11b=0
a = -10; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-10)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-10}=\frac{-22}{-20} =1+1/10 $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-10}=\frac{0}{-20} =0 $
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