5/2x-7/2=3/4x+14

Solution for 5/2x-7/2=3/4x+14 equation:

5/2x-7/2=3/4x+14

We move all terms to the left:

5/2x-7/2-(3/4x+14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+14)!=0

x∈R


We get rid of parentheses

5/2x-3/4x-14-7/2=0

We calculate fractions


20x/32x^2+(-24x)/32x^2+(-28x)/32x^2-14=0

We multiply all the terms by the denominator


20x+(-24x)+(-28x)-14*32x^2=0

Wy multiply elements

-448x^2+20x+(-24x)+(-28x)=0

We get rid of parentheses

-448x^2+20x-24x-28x=0

We add all the numbers together, and all the variables

-448x^2-32x=0

a = -448; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-448)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-448}=\frac{0}{-896}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-448}=\frac{64}{-896}
=-1/14
$