45x-13=1/8x

Solution for 45x-13=1/8x equation:

45x-13=1/8x

We move all terms to the left:

45x-13-(1/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

45x-(+1/8x)-13=0

We get rid of parentheses

45x-1/8x-13=0

We multiply all the terms by the denominator


45x*8x-13*8x-1=0

Wy multiply elements

360x^2-104x-1=0

a = 360; b = -104; c = -1;
Δ = b2-4ac
Δ = -1042-4·360·(-1)
Δ = 12256
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:

$\sqrt{\Delta}=\sqrt{12256}=\sqrt{16*766}=\sqrt{16}*\sqrt{766}=4\sqrt{766}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{766}}{2*360}=\frac{104-4\sqrt{766}}{720}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{766}}{2*360}=\frac{104+4\sqrt{766}}{720}
$