-2+3/4x-8=6-1/2x

Solution for -2+3/4x-8=6-1/2x equation:

-2+3/4x-8=6-1/2x

We move all terms to the left:

-2+3/4x-8-(6-1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(-1/2x+6)-2-8=0

We add all the numbers together, and all the variables

3/4x-(-1/2x+6)-10=0

We get rid of parentheses

3/4x+1/2x-6-10=0

We calculate fractions


6x/8x^2+4x/8x^2-6-10=0

We add all the numbers together, and all the variables

6x/8x^2+4x/8x^2-16=0

We multiply all the terms by the denominator


6x+4x-16*8x^2=0

We add all the numbers together, and all the variables

10x-16*8x^2=0

Wy multiply elements

-128x^2+10x=0

a = -128; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-128)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-128}=\frac{-20}{-256}
=5/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-128}=\frac{0}{-256}
=0
$