(5/6)b=15/8

Solution for (5/6)b=15/8 equation:

(5/6)b=15/8

We move all terms to the left:

(5/6)b-(15/8)=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-(+15/8)=0

We multiply parentheses

5b^2-(+15/8)=0

We get rid of parentheses

5b^2-15/8=0

We multiply all the terms by the denominator


5b^2*8-15=0

Wy multiply elements

40b^2-15=0

a = 40; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·40·(-15)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*40}=\frac{0-20\sqrt{6}}{80}
=-\frac{20\sqrt{6}}{80}
=-\frac{\sqrt{6}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*40}=\frac{0+20\sqrt{6}}{80}
=\frac{20\sqrt{6}}{80}
=\frac{\sqrt{6}}{4}
$