-1/2u+6=8-3/4u

Solution for -1/2u+6=8-3/4u equation:

-1/2u+6=8-3/4u

We move all terms to the left:

-1/2u+6-(8-3/4u)=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+8)+6=0

We get rid of parentheses

-1/2u+3/4u-8+6=0

We calculate fractions


(-4u)/8u^2+6u/8u^2-8+6=0

We add all the numbers together, and all the variables

(-4u)/8u^2+6u/8u^2-2=0

We multiply all the terms by the denominator


(-4u)+6u-2*8u^2=0

We add all the numbers together, and all the variables

6u+(-4u)-2*8u^2=0

Wy multiply elements

-16u^2+6u+(-4u)=0

We get rid of parentheses

-16u^2+6u-4u=0

We add all the numbers together, and all the variables

-16u^2+2u=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$