b(71/2)=5/6

Solution for b(71/2)=5/6 equation:

b(71/2)=5/6

We move all terms to the left:

b(71/2)-(5/6)=0

We add all the numbers together, and all the variables

b(+71/2)-(+5/6)=0

We multiply parentheses

71b^2-(+5/6)=0

We get rid of parentheses

71b^2-5/6=0

We multiply all the terms by the denominator


71b^2*6-5=0

Wy multiply elements

426b^2-5=0

a = 426; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·426·(-5)
Δ = 8520
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:

$\sqrt{\Delta}=\sqrt{8520}=\sqrt{4*2130}=\sqrt{4}*\sqrt{2130}=2\sqrt{2130}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{2130}}{2*426}=\frac{0-2\sqrt{2130}}{852}
=-\frac{2\sqrt{2130}}{852}
=-\frac{\sqrt{2130}}{426}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{2130}}{2*426}=\frac{0+2\sqrt{2130}}{852}
=\frac{2\sqrt{2130}}{852}
=\frac{\sqrt{2130}}{426}
$