1/4x+32=x+16

Solution for 1/4x+32=x+16 equation:

1/4x+32=x+16

We move all terms to the left:

1/4x+32-(x+16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x-16+32=0

We multiply all the terms by the denominator


-x*4x-16*4x+32*4x+1=0

Wy multiply elements

-4x^2-64x+128x+1=0

We add all the numbers together, and all the variables

-4x^2+64x+1=0

a = -4; b = 64; c = +1;
Δ = b2-4ac
Δ = 642-4·(-4)·1
Δ = 4112
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:

$\sqrt{\Delta}=\sqrt{4112}=\sqrt{16*257}=\sqrt{16}*\sqrt{257}=4\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{257}}{2*-4}=\frac{-64-4\sqrt{257}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{257}}{2*-4}=\frac{-64+4\sqrt{257}}{-8}
$