5/2x-7=3/4x+1

Solution for 5/2x-7=3/4x+1 equation:

5/2x-7=3/4x+1

We move all terms to the left:

5/2x-7-(3/4x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

5/2x-3/4x-1-7=0

We calculate fractions


20x/8x^2+(-6x)/8x^2-1-7=0

We add all the numbers together, and all the variables

20x/8x^2+(-6x)/8x^2-8=0

We multiply all the terms by the denominator


20x+(-6x)-8*8x^2=0

Wy multiply elements

-64x^2+20x+(-6x)=0

We get rid of parentheses

-64x^2+20x-6x=0

We add all the numbers together, and all the variables

-64x^2+14x=0

a = -64; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-64)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-64}=\frac{-28}{-128}
=7/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-64}=\frac{0}{-128}
=0
$