8-7/10b=6-1/5b

Solution for 8-7/10b=6-1/5b equation:

8-7/10b=6-1/5b

We move all terms to the left:

8-7/10b-(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)+8=0

We get rid of parentheses

-7/10b+1/5b-6+8=0

We calculate fractions


(-35b)/50b^2+10b/50b^2-6+8=0

We add all the numbers together, and all the variables

(-35b)/50b^2+10b/50b^2+2=0

We multiply all the terms by the denominator


(-35b)+10b+2*50b^2=0

We add all the numbers together, and all the variables

10b+(-35b)+2*50b^2=0

Wy multiply elements

100b^2+10b+(-35b)=0

We get rid of parentheses

100b^2+10b-35b=0

We add all the numbers together, and all the variables

100b^2-25b=0

a = 100; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·100·0
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*100}=\frac{0}{200}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*100}=\frac{50}{200}
=1/4
$