-4(2x-3)=8(-1/4x-2)

Solution for -4(2x-3)=8(-1/4x-2) equation:

-4(2x-3)=8(-1/4x-2)

We move all terms to the left:

-4(2x-3)-(8(-1/4x-2))=0


Domain of the equation: 4x-2))!=0

x∈R


We multiply parentheses

-8x-(8(-1/4x-2))+12=0

We multiply all the terms by the denominator


-8x*4x+12*4x-1-2))-(8(-2))=0

We add all the numbers together, and all the variables

-8x*4x+12*4x=0

Wy multiply elements

-32x^2+48x=0

a = -32; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-32)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-32}=\frac{-96}{-64}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-32}=\frac{0}{-64}
=0
$