3x-6+7x-2x/x=4

Solution for 3x-6+7x-2x/x=4 equation:

3x-6+7x-2x/x=4

We move all terms to the left:

3x-6+7x-2x/x-(4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

10x-2x/x-10=0

We multiply all the terms by the denominator


10x*x-2x-10*x=0

We add all the numbers together, and all the variables

-12x+10x*x=0

Wy multiply elements

10x^2-12x=0

a = 10; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·10·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*10}=\frac{24}{20}
=1+1/5
$