1/8x+4=9x

Solution for 1/8x+4=9x equation:

1/8x+4=9x

We move all terms to the left:

1/8x+4-(9x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-9x+1/8x+4=0

We multiply all the terms by the denominator


-9x*8x+4*8x+1=0

Wy multiply elements

-72x^2+32x+1=0

a = -72; b = 32; c = +1;
Δ = b2-4ac
Δ = 322-4·(-72)·1
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{82}}{2*-72}=\frac{-32-4\sqrt{82}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{82}}{2*-72}=\frac{-32+4\sqrt{82}}{-144}
$