6x+1/2x=240

Solution for 6x+1/2x=240 equation:

6x+1/2x=240

We move all terms to the left:

6x+1/2x-(240)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


6x*2x-240*2x+1=0

Wy multiply elements

12x^2-480x+1=0

a = 12; b = -480; c = +1;
Δ = b2-4ac
Δ = -4802-4·12·1
Δ = 230352
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:

$\sqrt{\Delta}=\sqrt{230352}=\sqrt{16*14397}=\sqrt{16}*\sqrt{14397}=4\sqrt{14397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-4\sqrt{14397}}{2*12}=\frac{480-4\sqrt{14397}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+4\sqrt{14397}}{2*12}=\frac{480+4\sqrt{14397}}{24}
$