7/4+4/3x=6-5/2x

Solution for 7/4+4/3x=6-5/2x equation:

7/4+4/3x=6-5/2x

We move all terms to the left:

7/4+4/3x-(6-5/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(-5/2x+6)+7/4=0

We get rid of parentheses

4/3x+5/2x-6+7/4=0

We calculate fractions


84x^2/96x^2+128x/96x^2+240x/96x^2-6=0

We multiply all the terms by the denominator


84x^2+128x+240x-6*96x^2=0

We add all the numbers together, and all the variables

84x^2+368x-6*96x^2=0

Wy multiply elements

84x^2-576x^2+368x=0

We add all the numbers together, and all the variables

-492x^2+368x=0

a = -492; b = 368; c = 0;
Δ = b2-4ac
Δ = 3682-4·(-492)·0
Δ = 135424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{135424}=368$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(368)-368}{2*-492}=\frac{-736}{-984}
=92/123
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(368)+368}{2*-492}=\frac{0}{-984}
=0
$