1/4x-3=0.5x+12

Solution for 1/4x-3=0.5x+12 equation:

1/4x-3=0.5x+12

We move all terms to the left:

1/4x-3-(0.5x+12)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-0.5x-12-3=0

We multiply all the terms by the denominator


-(0.5x)*4x-12*4x-3*4x+1=0

We add all the numbers together, and all the variables

-(+0.5x)*4x-12*4x-3*4x+1=0

We multiply parentheses

-0x^2-12*4x-3*4x+1=0

Wy multiply elements

-0x^2-48x-12x+1=0

We add all the numbers together, and all the variables

-1x^2-60x+1=0

a = -1; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·(-1)·1
Δ = 3604
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:

$\sqrt{\Delta}=\sqrt{3604}=\sqrt{4*901}=\sqrt{4}*\sqrt{901}=2\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{901}}{2*-1}=\frac{60-2\sqrt{901}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{901}}{2*-1}=\frac{60+2\sqrt{901}}{-2}
$