3/4x+1/2=-2/3x+9

Solution for 3/4x+1/2=-2/3x+9 equation:

3/4x+1/2=-2/3x+9

We move all terms to the left:

3/4x+1/2-(-2/3x+9)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x+9)!=0

x∈R


We get rid of parentheses

3/4x+2/3x-9+1/2=0

We calculate fractions


36x^2/48x^2+36x/48x^2+32x/48x^2-9=0

We multiply all the terms by the denominator


36x^2+36x+32x-9*48x^2=0

We add all the numbers together, and all the variables

36x^2+68x-9*48x^2=0

Wy multiply elements

36x^2-432x^2+68x=0

We add all the numbers together, and all the variables

-396x^2+68x=0

a = -396; b = 68; c = 0;
Δ = b2-4ac
Δ = 682-4·(-396)·0
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-68}{2*-396}=\frac{-136}{-792}
=17/99
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+68}{2*-396}=\frac{0}{-792}
=0
$