1/4x+32=-2x+4

Solution for 1/4x+32=-2x+4 equation:

1/4x+32=-2x+4

We move all terms to the left:

1/4x+32-(-2x+4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x+2x-4+32=0

We multiply all the terms by the denominator


2x*4x-4*4x+32*4x+1=0

Wy multiply elements

8x^2-16x+128x+1=0

We add all the numbers together, and all the variables

8x^2+112x+1=0

a = 8; b = 112; c = +1;
Δ = b2-4ac
Δ = 1122-4·8·1
Δ = 12512
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:

$\sqrt{\Delta}=\sqrt{12512}=\sqrt{16*782}=\sqrt{16}*\sqrt{782}=4\sqrt{782}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{782}}{2*8}=\frac{-112-4\sqrt{782}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{782}}{2*8}=\frac{-112+4\sqrt{782}}{16}
$