12x+1/2x=230

Solution for 12x+1/2x=230 equation:

12x+1/2x=230

We move all terms to the left:

12x+1/2x-(230)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


12x*2x-230*2x+1=0

Wy multiply elements

24x^2-460x+1=0

a = 24; b = -460; c = +1;
Δ = b2-4ac
Δ = -4602-4·24·1
Δ = 211504
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:

$\sqrt{\Delta}=\sqrt{211504}=\sqrt{16*13219}=\sqrt{16}*\sqrt{13219}=4\sqrt{13219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-460)-4\sqrt{13219}}{2*24}=\frac{460-4\sqrt{13219}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-460)+4\sqrt{13219}}{2*24}=\frac{460+4\sqrt{13219}}{48}
$