X=3x-10/8x

Solution for X=3x-10/8x equation:

X=3X-10/8X

We move all terms to the left:

X-(3X-10/8X)=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-(+3X-10/8X)=0

We get rid of parentheses

X-3X+10/8X=0

We multiply all the terms by the denominator


X*8X-3X*8X+10=0

Wy multiply elements

8X^2-24X^2+10=0

We add all the numbers together, and all the variables

-16X^2+10=0

a = -16; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-16)·10
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{10}}{2*-16}=\frac{0-8\sqrt{10}}{-32}
=-\frac{8\sqrt{10}}{-32}
=-\frac{\sqrt{10}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{10}}{2*-16}=\frac{0+8\sqrt{10}}{-32}
=\frac{8\sqrt{10}}{-32}
=\frac{\sqrt{10}}{-4}
$