X+8=1/4x+32

Solution for X+8=1/4x+32 equation:

X+8=1/4X+32

We move all terms to the left:

X+8-(1/4X+32)=0


Domain of the equation: 4X+32)!=0

X∈R


We get rid of parentheses

X-1/4X-32+8=0

We multiply all the terms by the denominator


X*4X-32*4X+8*4X-1=0

Wy multiply elements

4X^2-128X+32X-1=0

We add all the numbers together, and all the variables

4X^2-96X-1=0

a = 4; b = -96; c = -1;
Δ = b2-4ac
Δ = -962-4·4·(-1)
Δ = 9232
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:

$\sqrt{\Delta}=\sqrt{9232}=\sqrt{16*577}=\sqrt{16}*\sqrt{577}=4\sqrt{577}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{577}}{2*4}=\frac{96-4\sqrt{577}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{577}}{2*4}=\frac{96+4\sqrt{577}}{8}
$