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b/3b+4=2b+6b-16
We move all terms to the left:
b/3b+4-(2b+6b-16)=0
Domain of the equation: 3b!=0We add all the numbers together, and all the variables
b!=0/3
b!=0
b∈R
b/3b-(8b-16)+4=0
We get rid of parentheses
b/3b-8b+16+4=0
We multiply all the terms by the denominator
b-8b*3b+16*3b+4*3b=0
Wy multiply elements
-24b^2+b+48b+12b=0
We add all the numbers together, and all the variables
-24b^2+61b=0
a = -24; b = 61; c = 0;
Δ = b2-4ac
Δ = 612-4·(-24)·0
Δ = 3721
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{3721}=61$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-61}{2*-24}=\frac{-122}{-48} =2+13/24 $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+61}{2*-24}=\frac{0}{-48} =0 $
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