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

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

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

We move all terms to the left:

4/3x-5/2-(-3/4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-240x^2)/48x^2+64x/48x^2+36x/48x^2=0

We multiply all the terms by the denominator


(-240x^2)+64x+36x=0

We add all the numbers together, and all the variables

(-240x^2)+100x=0

We get rid of parentheses

-240x^2+100x=0

a = -240; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-240)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-240}=\frac{-200}{-480}
=5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-240}=\frac{0}{-480}
=0
$