6x+1/8x=109

Solution for 6x+1/8x=109 equation:

6x+1/8x=109

We move all terms to the left:

6x+1/8x-(109)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


6x*8x-109*8x+1=0

Wy multiply elements

48x^2-872x+1=0

a = 48; b = -872; c = +1;
Δ = b2-4ac
Δ = -8722-4·48·1
Δ = 760192
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:

$\sqrt{\Delta}=\sqrt{760192}=\sqrt{64*11878}=\sqrt{64}*\sqrt{11878}=8\sqrt{11878}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-872)-8\sqrt{11878}}{2*48}=\frac{872-8\sqrt{11878}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-872)+8\sqrt{11878}}{2*48}=\frac{872+8\sqrt{11878}}{96}
$