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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


64x^2/72x^2+(-252x)/72x^2+(-90x)/72x^2+4=0

We multiply all the terms by the denominator


64x^2+(-252x)+(-90x)+4*72x^2=0

Wy multiply elements

64x^2+288x^2+(-252x)+(-90x)=0

We get rid of parentheses

64x^2+288x^2-252x-90x=0

We add all the numbers together, and all the variables

352x^2-342x=0

a = 352; b = -342; c = 0;
Δ = b2-4ac
Δ = -3422-4·352·0
Δ = 116964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{116964}=342$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-342}{2*352}=\frac{0}{704}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+342}{2*352}=\frac{684}{704}
=171/176
$