3/4x-2(x-1)=1/4x+5

Solution for 3/4x-2(x-1)=1/4x+5 equation:

3/4x-2(x-1)=1/4x+5

We move all terms to the left:

3/4x-2(x-1)-(1/4x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We multiply parentheses

3/4x-2x-(1/4x+5)+2=0

We get rid of parentheses

3/4x-2x-1/4x-5+2=0

We multiply all the terms by the denominator


-2x*4x-5*4x+2*4x+3-1=0

We add all the numbers together, and all the variables

-2x*4x-5*4x+2*4x+2=0

Wy multiply elements

-8x^2-20x+8x+2=0

We add all the numbers together, and all the variables

-8x^2-12x+2=0

a = -8; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-8)·2
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*-8}=\frac{12-4\sqrt{13}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*-8}=\frac{12+4\sqrt{13}}{-16}
$