3/4x+18/4=6-2/3x

Solution for 3/4x+18/4=6-2/3x equation:

3/4x+18/4=6-2/3x

We move all terms to the left:

3/4x+18/4-(6-2/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-2/3x+6)+18/4=0

We get rid of parentheses

3/4x+2/3x-6+18/4=0

We calculate fractions


9x/192x^2+128x/192x^2+54x/192x^2-6=0

We multiply all the terms by the denominator


9x+128x+54x-6*192x^2=0

We add all the numbers together, and all the variables

191x-6*192x^2=0

Wy multiply elements

-1152x^2+191x=0

a = -1152; b = 191; c = 0;
Δ = b2-4ac
Δ = 1912-4·(-1152)·0
Δ = 36481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36481}=191$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(191)-191}{2*-1152}=\frac{-382}{-2304}
=191/1152
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(191)+191}{2*-1152}=\frac{0}{-2304}
=0
$