u(1/8)=5/6

Solution for u(1/8)=5/6 equation:

u(1/8)=5/6

We move all terms to the left:

u(1/8)-(5/6)=0

We add all the numbers together, and all the variables

u(+1/8)-(+5/6)=0

We multiply parentheses

u^2-(+5/6)=0

We get rid of parentheses

u^2-5/6=0

We multiply all the terms by the denominator


u^2*6-5=0

Wy multiply elements

6u^2-5=0

a = 6; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·6·(-5)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*6}=\frac{0-2\sqrt{30}}{12}
=-\frac{2\sqrt{30}}{12}
=-\frac{\sqrt{30}}{6}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*6}=\frac{0+2\sqrt{30}}{12}
=\frac{2\sqrt{30}}{12}
=\frac{\sqrt{30}}{6}
$