16x-7/12x+1=1

Solution for 16x-7/12x+1=1 equation:

16x-7/12x+1=1

We move all terms to the left:

16x-7/12x+1-(1)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

16x-7/12x=0

We multiply all the terms by the denominator


16x*12x-7=0

Wy multiply elements

192x^2-7=0

a = 192; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·192·(-7)
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{21}}{2*192}=\frac{0-16\sqrt{21}}{384}
=-\frac{16\sqrt{21}}{384}
=-\frac{\sqrt{21}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{21}}{2*192}=\frac{0+16\sqrt{21}}{384}
=\frac{16\sqrt{21}}{384}
=\frac{\sqrt{21}}{24}
$