1/2u-2=-5+u

Solution for 1/2u-2=-5+u equation:

1/2u-2=-5+u

We move all terms to the left:

1/2u-2-(-5+u)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R


We add all the numbers together, and all the variables

1/2u-(u-5)-2=0

We get rid of parentheses

1/2u-u+5-2=0

We multiply all the terms by the denominator


-u*2u+5*2u-2*2u+1=0

Wy multiply elements

-2u^2+10u-4u+1=0

We add all the numbers together, and all the variables

-2u^2+6u+1=0

a = -2; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-2)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{11}}{2*-2}=\frac{-6-2\sqrt{11}}{-4}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{11}}{2*-2}=\frac{-6+2\sqrt{11}}{-4}
$