6x+1/2x=58

Solution for 6x+1/2x=58 equation:

6x+1/2x=58

We move all terms to the left:

6x+1/2x-(58)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


6x*2x-58*2x+1=0

Wy multiply elements

12x^2-116x+1=0

a = 12; b = -116; c = +1;
Δ = b2-4ac
Δ = -1162-4·12·1
Δ = 13408
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:

$\sqrt{\Delta}=\sqrt{13408}=\sqrt{16*838}=\sqrt{16}*\sqrt{838}=4\sqrt{838}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-4\sqrt{838}}{2*12}=\frac{116-4\sqrt{838}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+4\sqrt{838}}{2*12}=\frac{116+4\sqrt{838}}{24}
$