2/3u+7=3/4u+9

Solution for 2/3u+7=3/4u+9 equation:

2/3u+7=3/4u+9

We move all terms to the left:

2/3u+7-(3/4u+9)=0


Domain of the equation: 3u!=0

u!=0/3

u!=0

u∈R



Domain of the equation: 4u+9)!=0

u∈R


We get rid of parentheses

2/3u-3/4u-9+7=0

We calculate fractions


8u/12u^2+(-9u)/12u^2-9+7=0

We add all the numbers together, and all the variables

8u/12u^2+(-9u)/12u^2-2=0

We multiply all the terms by the denominator


8u+(-9u)-2*12u^2=0

Wy multiply elements

-24u^2+8u+(-9u)=0

We get rid of parentheses

-24u^2+8u-9u=0

We add all the numbers together, and all the variables

-24u^2-1u=0

a = -24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-24)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-24}=\frac{0}{-48}
=0
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-24}=\frac{2}{-48}
=-1/24
$