.25x-2=-6+5/12x

Solution for .25x-2=-6+5/12x equation:

.25x-2=-6+5/12x

We move all terms to the left:

.25x-2-(-6+5/12x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

.25x-(5/12x-6)-2=0

We get rid of parentheses

.25x-5/12x+6-2=0

We multiply all the terms by the denominator


(.25x)*12x+6*12x-2*12x-5=0

We add all the numbers together, and all the variables

(+.25x)*12x+6*12x-2*12x-5=0

We multiply parentheses

12x^2+6*12x-2*12x-5=0

Wy multiply elements

12x^2+72x-24x-5=0

We add all the numbers together, and all the variables

12x^2+48x-5=0

a = 12; b = 48; c = -5;
Δ = b2-4ac
Δ = 482-4·12·(-5)
Δ = 2544
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:

$\sqrt{\Delta}=\sqrt{2544}=\sqrt{16*159}=\sqrt{16}*\sqrt{159}=4\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{159}}{2*12}=\frac{-48-4\sqrt{159}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{159}}{2*12}=\frac{-48+4\sqrt{159}}{24}
$