17x-12=114/3x

Solution for 17x-12=114/3x equation:

17x-12=114/3x

We move all terms to the left:

17x-12-(114/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

17x-(+114/3x)-12=0

We get rid of parentheses

17x-114/3x-12=0

We multiply all the terms by the denominator


17x*3x-12*3x-114=0

Wy multiply elements

51x^2-36x-114=0

a = 51; b = -36; c = -114;
Δ = b2-4ac
Δ = -362-4·51·(-114)
Δ = 24552
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:

$\sqrt{\Delta}=\sqrt{24552}=\sqrt{36*682}=\sqrt{36}*\sqrt{682}=6\sqrt{682}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{682}}{2*51}=\frac{36-6\sqrt{682}}{102}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{682}}{2*51}=\frac{36+6\sqrt{682}}{102}
$