1/4(x)=12x-2

Solution for 1/4(x)=12x-2 equation:

1/4(x)=12x-2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-12x+2=0

We multiply all the terms by the denominator


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

Wy multiply elements

-48x^2+8x+1=0

a = -48; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-48)·1
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*-48}=\frac{-24}{-96}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*-48}=\frac{8}{-96}
=-1/12
$