3x+(1/2x)=914

Solution for 3x+(1/2x)=914 equation:

3x+(1/2x)=914

We move all terms to the left:

3x+(1/2x)-(914)=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+(+1/2x)-914=0

We get rid of parentheses

3x+1/2x-914=0

We multiply all the terms by the denominator


3x*2x-914*2x+1=0

Wy multiply elements

6x^2-1828x+1=0

a = 6; b = -1828; c = +1;
Δ = b2-4ac
Δ = -18282-4·6·1
Δ = 3341560
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:

$\sqrt{\Delta}=\sqrt{3341560}=\sqrt{4*835390}=\sqrt{4}*\sqrt{835390}=2\sqrt{835390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1828)-2\sqrt{835390}}{2*6}=\frac{1828-2\sqrt{835390}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1828)+2\sqrt{835390}}{2*6}=\frac{1828+2\sqrt{835390}}{12}
$