(5/6)b=17/8

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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} $

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