2+7/10b=6+1/5b

Solution for 2+7/10b=6+1/5b equation:

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)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

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
$