3x-14=61/2x

Solution for 3x-14=61/2x equation:

3x-14=61/2x

We move all terms to the left:

3x-14-(61/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+61/2x)-14=0

We get rid of parentheses

3x-61/2x-14=0

We multiply all the terms by the denominator


3x*2x-14*2x-61=0

Wy multiply elements

6x^2-28x-61=0

a = 6; b = -28; c = -61;
Δ = b2-4ac
Δ = -282-4·6·(-61)
Δ = 2248
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:

$\sqrt{\Delta}=\sqrt{2248}=\sqrt{4*562}=\sqrt{4}*\sqrt{562}=2\sqrt{562}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{562}}{2*6}=\frac{28-2\sqrt{562}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{562}}{2*6}=\frac{28+2\sqrt{562}}{12}
$