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

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

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

We move all terms to the left:

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

We calculate fractions


(28x+5)/8x^2+(-6x)/8x^2-14=0

We multiply all the terms by the denominator


(28x+5)+(-6x)-14*8x^2=0

Wy multiply elements

-112x^2+(28x+5)+(-6x)=0

We get rid of parentheses

-112x^2+28x-6x+5=0

We add all the numbers together, and all the variables

-112x^2+22x+5=0

a = -112; b = 22; c = +5;
Δ = b2-4ac
Δ = 222-4·(-112)·5
Δ = 2724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2724}=\sqrt{4*681}=\sqrt{4}*\sqrt{681}=2\sqrt{681}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{681}}{2*-112}=\frac{-22-2\sqrt{681}}{-224}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{681}}{2*-112}=\frac{-22+2\sqrt{681}}{-224}
$