3x+1/2x=279

Solution for 3x+1/2x=279 equation:

3x+1/2x=279

We move all terms to the left:

3x+1/2x-(279)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-279*2x+1=0

Wy multiply elements

6x^2-558x+1=0

a = 6; b = -558; c = +1;
Δ = b2-4ac
Δ = -5582-4·6·1
Δ = 311340
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:

$\sqrt{\Delta}=\sqrt{311340}=\sqrt{4*77835}=\sqrt{4}*\sqrt{77835}=2\sqrt{77835}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-558)-2\sqrt{77835}}{2*6}=\frac{558-2\sqrt{77835}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-558)+2\sqrt{77835}}{2*6}=\frac{558+2\sqrt{77835}}{12}
$