X/2x+72=32x-14

Solution for X/2x+72=32x-14 equation:

X/2X+72=32X-14

We move all terms to the left:

X/2X+72-(32X-14)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We get rid of parentheses

X/2X-32X+14+72=0

We multiply all the terms by the denominator


X-32X*2X+14*2X+72*2X=0

Wy multiply elements

-64X^2+X+28X+144X=0

We add all the numbers together, and all the variables

-64X^2+173X=0

a = -64; b = 173; c = 0;
Δ = b2-4ac
Δ = 1732-4·(-64)·0
Δ = 29929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29929}=173$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(173)-173}{2*-64}=\frac{-346}{-128}
=2+45/64
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(173)+173}{2*-64}=\frac{0}{-128}
=0
$