3x+5/2x=8x-14

Solution for 3x+5/2x=8x-14 equation:

3x+5/2x=8x-14

We move all terms to the left:

3x+5/2x-(8x-14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3x+5/2x-8x+14=0

We multiply all the terms by the denominator


3x*2x-8x*2x+14*2x+5=0

Wy multiply elements

6x^2-16x^2+28x+5=0

We add all the numbers together, and all the variables

-10x^2+28x+5=0

a = -10; b = 28; c = +5;
Δ = b2-4ac
Δ = 282-4·(-10)·5
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{246}}{2*-10}=\frac{-28-2\sqrt{246}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{246}}{2*-10}=\frac{-28+2\sqrt{246}}{-20}
$