-1/4*12x-20=5-3x

Solution for -1/4*12x-20=5-3x equation:

-1/4*12x-20=5-3x

We move all terms to the left:

-1/4*12x-20-(5-3x)=0


Domain of the equation: 4*12x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/4*12x-(-3x+5)-20=0

We get rid of parentheses

-1/4*12x+3x-5-20=0

We multiply all the terms by the denominator


3x*4*12x-5*4*12x-20*4*12x-1=0

Wy multiply elements

144x^2*1-240x*1-960x*1-1=0

Wy multiply elements

144x^2-240x-960x-1=0

We add all the numbers together, and all the variables

144x^2-1200x-1=0

a = 144; b = -1200; c = -1;
Δ = b2-4ac
Δ = -12002-4·144·(-1)
Δ = 1440576
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:

$\sqrt{\Delta}=\sqrt{1440576}=\sqrt{576*2501}=\sqrt{576}*\sqrt{2501}=24\sqrt{2501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-24\sqrt{2501}}{2*144}=\frac{1200-24\sqrt{2501}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+24\sqrt{2501}}{2*144}=\frac{1200+24\sqrt{2501}}{288}
$