x-8=3/5x

Solution for x-8=3/5x equation:

x-8=3/5x

We move all terms to the left:

x-8-(3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+3/5x)-8=0

We get rid of parentheses

x-3/5x-8=0

We multiply all the terms by the denominator


x*5x-8*5x-3=0

Wy multiply elements

5x^2-40x-3=0

a = 5; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·5·(-3)
Δ = 1660
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:

$\sqrt{\Delta}=\sqrt{1660}=\sqrt{4*415}=\sqrt{4}*\sqrt{415}=2\sqrt{415}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{415}}{2*5}=\frac{40-2\sqrt{415}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{415}}{2*5}=\frac{40+2\sqrt{415}}{10}
$