(31/15)b=4/5

Solution for (31/15)b=4/5 equation:

(31/15)b=4/5

We move all terms to the left:

(31/15)b-(4/5)=0


Domain of the equation: 15)b!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

(+31/15)b-(+4/5)=0

We multiply parentheses

31b^2-(+4/5)=0

We get rid of parentheses

31b^2-4/5=0

We multiply all the terms by the denominator


31b^2*5-4=0

Wy multiply elements

155b^2-4=0

a = 155; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·155·(-4)
Δ = 2480
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:

$\sqrt{\Delta}=\sqrt{2480}=\sqrt{16*155}=\sqrt{16}*\sqrt{155}=4\sqrt{155}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{155}}{2*155}=\frac{0-4\sqrt{155}}{310}
=-\frac{4\sqrt{155}}{310}
=-\frac{2\sqrt{155}}{155}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{155}}{2*155}=\frac{0+4\sqrt{155}}{310}
=\frac{4\sqrt{155}}{310}
=\frac{2\sqrt{155}}{155}
$