1/8x+9=6x+11

Solution for 1/8x+9=6x+11 equation:

1/8x+9=6x+11

We move all terms to the left:

1/8x+9-(6x+11)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

1/8x-6x-11+9=0

We multiply all the terms by the denominator


-6x*8x-11*8x+9*8x+1=0

Wy multiply elements

-48x^2-88x+72x+1=0

We add all the numbers together, and all the variables

-48x^2-16x+1=0

a = -48; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-48)·1
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{7}}{2*-48}=\frac{16-8\sqrt{7}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{7}}{2*-48}=\frac{16+8\sqrt{7}}{-96}
$