x-33=5/8x

Solution for x-33=5/8x equation:

x-33=5/8x

We move all terms to the left:

x-33-(5/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+5/8x)-33=0

We get rid of parentheses

x-5/8x-33=0

We multiply all the terms by the denominator


x*8x-33*8x-5=0

Wy multiply elements

8x^2-264x-5=0

a = 8; b = -264; c = -5;
Δ = b2-4ac
Δ = -2642-4·8·(-5)
Δ = 69856
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:

$\sqrt{\Delta}=\sqrt{69856}=\sqrt{16*4366}=\sqrt{16}*\sqrt{4366}=4\sqrt{4366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-4\sqrt{4366}}{2*8}=\frac{264-4\sqrt{4366}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+4\sqrt{4366}}{2*8}=\frac{264+4\sqrt{4366}}{16}
$