X+8=1/4x+31

Solution for X+8=1/4x+31 equation:

X+8=1/4X+31

We move all terms to the left:

X+8-(1/4X+31)=0


Domain of the equation: 4X+31)!=0

X∈R


We get rid of parentheses

X-1/4X-31+8=0

We multiply all the terms by the denominator


X*4X-31*4X+8*4X-1=0

Wy multiply elements

4X^2-124X+32X-1=0

We add all the numbers together, and all the variables

4X^2-92X-1=0

a = 4; b = -92; c = -1;
Δ = b2-4ac
Δ = -922-4·4·(-1)
Δ = 8480
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:

$\sqrt{\Delta}=\sqrt{8480}=\sqrt{16*530}=\sqrt{16}*\sqrt{530}=4\sqrt{530}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{530}}{2*4}=\frac{92-4\sqrt{530}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{530}}{2*4}=\frac{92+4\sqrt{530}}{8}
$