2x-33=5/8x

Solution for 2x-33=5/8x equation:

2x-33=5/8x

We move all terms to the left:

2x-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

2x-(+5/8x)-33=0

We get rid of parentheses

2x-5/8x-33=0

We multiply all the terms by the denominator


2x*8x-33*8x-5=0

Wy multiply elements

16x^2-264x-5=0

a = 16; b = -264; c = -5;
Δ = b2-4ac
Δ = -2642-4·16·(-5)
Δ = 70016
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:

$\sqrt{\Delta}=\sqrt{70016}=\sqrt{64*1094}=\sqrt{64}*\sqrt{1094}=8\sqrt{1094}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-8\sqrt{1094}}{2*16}=\frac{264-8\sqrt{1094}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+8\sqrt{1094}}{2*16}=\frac{264+8\sqrt{1094}}{32}
$