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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*4x+2*4x+1+3=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-8x^2+8x+4=0

a = -8; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-8)·4
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{3}}{2*-8}=\frac{-8-8\sqrt{3}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{3}}{2*-8}=\frac{-8+8\sqrt{3}}{-16}
$