-b=5/8b-2b

Solution for -b=5/8b-2b equation:

-b=5/8b-2b

We move all terms to the left:

-b-(5/8b-2b)=0


Domain of the equation: 8b-2b)!=0

b∈R


We add all the numbers together, and all the variables

-b-(-2b+5/8b)=0

We add all the numbers together, and all the variables

-1b-(-2b+5/8b)=0

We get rid of parentheses

-1b+2b-5/8b=0

We multiply all the terms by the denominator


-1b*8b+2b*8b-5=0

Wy multiply elements

-8b^2+16b^2-5=0

We add all the numbers together, and all the variables

8b^2-5=0

a = 8; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·8·(-5)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*8}=\frac{0-4\sqrt{10}}{16}
=-\frac{4\sqrt{10}}{16}
=-\frac{\sqrt{10}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*8}=\frac{0+4\sqrt{10}}{16}
=\frac{4\sqrt{10}}{16}
=\frac{\sqrt{10}}{4}
$