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

Solution for 3/4x-2=6+1/10x equation:

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


30x/40x^2+(-4x)/40x^2-6-2=0

We add all the numbers together, and all the variables

30x/40x^2+(-4x)/40x^2-8=0

We multiply all the terms by the denominator


30x+(-4x)-8*40x^2=0

Wy multiply elements

-320x^2+30x+(-4x)=0

We get rid of parentheses

-320x^2+30x-4x=0

We add all the numbers together, and all the variables

-320x^2+26x=0

a = -320; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-320)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-320}=\frac{-52}{-640}
=13/160
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-320}=\frac{0}{-640}
=0
$