3/8x-3(2)-1/4x+1/8x=12

Solution for 3/8x-3(2)-1/4x+1/8x=12 equation:

3/8x-3(2)-1/4x+1/8x=12

We move all terms to the left:

3/8x-3(2)-1/4x+1/8x-(12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x-1/4x+1/8x-44=0

We calculate fractions


(4x+3)/32x^2+(-8x)/32x^2-44=0

We multiply all the terms by the denominator


(4x+3)+(-8x)-44*32x^2=0

Wy multiply elements

-1408x^2+(4x+3)+(-8x)=0

We get rid of parentheses

-1408x^2+4x-8x+3=0

We add all the numbers together, and all the variables

-1408x^2-4x+3=0

a = -1408; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-1408)·3
Δ = 16912
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:

$\sqrt{\Delta}=\sqrt{16912}=\sqrt{16*1057}=\sqrt{16}*\sqrt{1057}=4\sqrt{1057}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{1057}}{2*-1408}=\frac{4-4\sqrt{1057}}{-2816}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{1057}}{2*-1408}=\frac{4+4\sqrt{1057}}{-2816}
$