-2b=-1/5b+2

Solution for -2b=-1/5b+2 equation:

-2b=-1/5b+2

We move all terms to the left:

-2b-(-1/5b+2)=0


Domain of the equation: 5b+2)!=0

b∈R


We get rid of parentheses

-2b+1/5b-2=0

We multiply all the terms by the denominator


-2b*5b-2*5b+1=0

Wy multiply elements

-10b^2-10b+1=0

a = -10; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·(-10)·1
Δ = 140
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{35}}{2*-10}=\frac{10-2\sqrt{35}}{-20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{35}}{2*-10}=\frac{10+2\sqrt{35}}{-20}
$