3/4x-19=7/2x+25

Solution for 3/4x-19=7/2x+25 equation:

3/4x-19=7/2x+25

We move all terms to the left:

3/4x-19-(7/2x+25)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+25)!=0

x∈R


We get rid of parentheses

3/4x-7/2x-25-19=0

We calculate fractions


6x/8x^2+(-28x)/8x^2-25-19=0

We add all the numbers together, and all the variables

6x/8x^2+(-28x)/8x^2-44=0

We multiply all the terms by the denominator


6x+(-28x)-44*8x^2=0

Wy multiply elements

-352x^2+6x+(-28x)=0

We get rid of parentheses

-352x^2+6x-28x=0

We add all the numbers together, and all the variables

-352x^2-22x=0

a = -352; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·(-352)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-22}{2*-352}=\frac{0}{-704}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*-352}=\frac{44}{-704}
=-1/16
$