1/4(16x)-2=7x+2-3x

Solution for 1/4(16x)-2=7x+2-3x equation:

1/4(16x)-2=7x+2-3x

We move all terms to the left:

1/4(16x)-2-(7x+2-3x)=0


Domain of the equation: 416x!=0

x!=0/416

x!=0

x∈R


We add all the numbers together, and all the variables

1/416x-(4x+2)-2=0

We get rid of parentheses

1/416x-4x-2-2=0

We multiply all the terms by the denominator


-4x*416x-2*416x-2*416x+1=0

Wy multiply elements

-1664x^2-832x-832x+1=0

We add all the numbers together, and all the variables

-1664x^2-1664x+1=0

a = -1664; b = -1664; c = +1;
Δ = b2-4ac
Δ = -16642-4·(-1664)·1
Δ = 2775552
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:

$\sqrt{\Delta}=\sqrt{2775552}=\sqrt{256*10842}=\sqrt{256}*\sqrt{10842}=16\sqrt{10842}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1664)-16\sqrt{10842}}{2*-1664}=\frac{1664-16\sqrt{10842}}{-3328}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1664)+16\sqrt{10842}}{2*-1664}=\frac{1664+16\sqrt{10842}}{-3328}
$