6x+1/8x=113

Solution for 6x+1/8x=113 equation:

6x+1/8x=113

We move all terms to the left:

6x+1/8x-(113)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


6x*8x-113*8x+1=0

Wy multiply elements

48x^2-904x+1=0

a = 48; b = -904; c = +1;
Δ = b2-4ac
Δ = -9042-4·48·1
Δ = 817024
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:

$\sqrt{\Delta}=\sqrt{817024}=\sqrt{64*12766}=\sqrt{64}*\sqrt{12766}=8\sqrt{12766}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-904)-8\sqrt{12766}}{2*48}=\frac{904-8\sqrt{12766}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-904)+8\sqrt{12766}}{2*48}=\frac{904+8\sqrt{12766}}{96}
$