5u-12/u-6=0

Solution for 5u-12/u-6=0 equation:

5u-12/u-6=0


Domain of the equation: u!=0

u∈R


We multiply all the terms by the denominator


5u*u-6*u-12=0

We add all the numbers together, and all the variables

-6u+5u*u-12=0

Wy multiply elements

5u^2-6u-12=0

a = 5; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·5·(-12)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*5}=\frac{6-2\sqrt{69}}{10}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*5}=\frac{6+2\sqrt{69}}{10}
$