(5/6)b=17/8

Solution for (5/6)b=17/8 equation:

(5/6)b=17/8

We move all terms to the left:

(5/6)b-(17/8)=0


Domain of the equation: 6)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

(+5/6)b-(+17/8)=0

We multiply parentheses

5b^2-(+17/8)=0

We get rid of parentheses

5b^2-17/8=0

We multiply all the terms by the denominator


5b^2*8-17=0

Wy multiply elements

40b^2-17=0

a = 40; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·40·(-17)
Δ = 2720
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:

$\sqrt{\Delta}=\sqrt{2720}=\sqrt{16*170}=\sqrt{16}*\sqrt{170}=4\sqrt{170}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{170}}{2*40}=\frac{0-4\sqrt{170}}{80}
=-\frac{4\sqrt{170}}{80}
=-\frac{\sqrt{170}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{170}}{2*40}=\frac{0+4\sqrt{170}}{80}
=\frac{4\sqrt{170}}{80}
=\frac{\sqrt{170}}{20}
$