1/2u-3=2-3/4u

Solution for 1/2u-3=2-3/4u equation:

1/2u-3=2-3/4u

We move all terms to the left:

1/2u-3-(2-3/4u)=0


Domain of the equation: 2u!=0

u!=0/2

u!=0

u∈R



Domain of the equation: 4u)!=0

u!=0/1

u!=0

u∈R


We add all the numbers together, and all the variables

1/2u-(-3/4u+2)-3=0

We get rid of parentheses

1/2u+3/4u-2-3=0

We calculate fractions


4u/8u^2+6u/8u^2-2-3=0

We add all the numbers together, and all the variables

4u/8u^2+6u/8u^2-5=0

We multiply all the terms by the denominator


4u+6u-5*8u^2=0

We add all the numbers together, and all the variables

10u-5*8u^2=0

Wy multiply elements

-40u^2+10u=0

a = -40; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-40)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-40}=\frac{-20}{-80}
=1/4
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-40}=\frac{0}{-80}
=0
$