x/4x-2(x-5)=-2+4x+2

Solution for x/4x-2(x-5)=-2+4x+2 equation:

x/4x-2(x-5)=-2+4x+2

We move all terms to the left:

x/4x-2(x-5)-(-2+4x+2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x/4x-2(x-5)-(+4x)=0

We multiply parentheses

x/4x-2x-(+4x)+10=0

We get rid of parentheses

x/4x-2x-4x+10=0

We multiply all the terms by the denominator


x-2x*4x-4x*4x+10*4x=0

Wy multiply elements

-8x^2-16x^2+x+40x=0

We add all the numbers together, and all the variables

-24x^2+41x=0

a = -24; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·(-24)·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*-24}=\frac{-82}{-48}
=1+17/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*-24}=\frac{0}{-48}
=0
$