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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)-1)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-6x^2)/24x+()/24x+324x/24x=0

We multiply all the terms by the denominator


(-6x^2)+324x+()=0

We add all the numbers together, and all the variables

(-6x^2)+324x=0

We get rid of parentheses

-6x^2+324x=0

a = -6; b = 324; c = 0;
Δ = b2-4ac
Δ = 3242-4·(-6)·0
Δ = 104976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{104976}=324$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-324}{2*-6}=\frac{-648}{-12}
=+54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+324}{2*-6}=\frac{0}{-12}
=0
$