8x-3x=1/2(10x)

Solution for 8x-3x=1/2(10x) equation:

8x-3x=1/2(10x)

We move all terms to the left:

8x-3x-(1/2(10x))=0


Domain of the equation: 210x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-3x-(+1/210x)=0

We add all the numbers together, and all the variables

5x-(+1/210x)=0

We get rid of parentheses

5x-1/210x=0

We multiply all the terms by the denominator


5x*210x-1=0

Wy multiply elements

1050x^2-1=0

a = 1050; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1050·(-1)
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{42}}{2*1050}=\frac{0-10\sqrt{42}}{2100}
=-\frac{10\sqrt{42}}{2100}
=-\frac{\sqrt{42}}{210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{42}}{2*1050}=\frac{0+10\sqrt{42}}{2100}
=\frac{10\sqrt{42}}{2100}
=\frac{\sqrt{42}}{210}
$