6u-5/6u+9=14

Solution for 6u-5/6u+9=14 equation:

6u-5/6u+9=14

We move all terms to the left:

6u-5/6u+9-(14)=0


Domain of the equation: 6u!=0

u!=0/6

u!=0

u∈R


We add all the numbers together, and all the variables

6u-5/6u-5=0

We multiply all the terms by the denominator


6u*6u-5*6u-5=0

Wy multiply elements

36u^2-30u-5=0

a = 36; b = -30; c = -5;
Δ = b2-4ac
Δ = -302-4·36·(-5)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{5}}{2*36}=\frac{30-18\sqrt{5}}{72}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{5}}{2*36}=\frac{30+18\sqrt{5}}{72}
$