-5/4x+9/2=-2/3x

Solution for -5/4x+9/2=-2/3x equation:

-5/4x+9/2=-2/3x

We move all terms to the left:

-5/4x+9/2-(-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 get rid of parentheses

-5/4x+2/3x+9/2=0

We calculate fractions


324x^2/48x^2+(-60x)/48x^2+32x/48x^2=0

We multiply all the terms by the denominator


324x^2+(-60x)+32x=0

We add all the numbers together, and all the variables

324x^2+32x+(-60x)=0

We get rid of parentheses

324x^2+32x-60x=0

We add all the numbers together, and all the variables

324x^2-28x=0

a = 324; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·324·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*324}=\frac{56}{648}
=7/81
$