-2/7b+1=2b-10

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

-2/7b+1=2b-10

We move all terms to the left:

-2/7b+1-(2b-10)=0


Domain of the equation: 7b!=0

b!=0/7

b!=0

b∈R


We get rid of parentheses

-2/7b-2b+10+1=0

We multiply all the terms by the denominator


-2b*7b+10*7b+1*7b-2=0

Wy multiply elements

-14b^2+70b+7b-2=0

We add all the numbers together, and all the variables

-14b^2+77b-2=0

a = -14; b = 77; c = -2;
Δ = b2-4ac
Δ = 772-4·(-14)·(-2)
Δ = 5817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-\sqrt{5817}}{2*-14}=\frac{-77-\sqrt{5817}}{-28}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+\sqrt{5817}}{2*-14}=\frac{-77+\sqrt{5817}}{-28}
$