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2+7/10b=6+1/5b
We move all terms to the left:
2+7/10b-(6+1/5b)=0
Domain of the equation: 10b!=0
b!=0/10
b!=0
b∈R
Domain of the equation: 5b)!=0We add all the numbers together, and all the variables
b!=0/1
b!=0
b∈R
7/10b-(1/5b+6)+2=0
We get rid of parentheses
7/10b-1/5b-6+2=0
We calculate fractions
35b/50b^2+(-10b)/50b^2-6+2=0
We add all the numbers together, and all the variables
35b/50b^2+(-10b)/50b^2-4=0
We multiply all the terms by the denominator
35b+(-10b)-4*50b^2=0
Wy multiply elements
-200b^2+35b+(-10b)=0
We get rid of parentheses
-200b^2+35b-10b=0
We add all the numbers together, and all the variables
-200b^2+25b=0
a = -200; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-200)·0
Δ = 625
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{625}=25$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-200}=\frac{-50}{-400} =1/8 $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-200}=\frac{0}{-400} =0 $
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