X+31=1/2x+20

Solution for X+31=1/2x+20 equation:

X+31=1/2X+20

We move all terms to the left:

X+31-(1/2X+20)=0


Domain of the equation: 2X+20)!=0

X∈R


We get rid of parentheses

X-1/2X-20+31=0

We multiply all the terms by the denominator


X*2X-20*2X+31*2X-1=0

Wy multiply elements

2X^2-40X+62X-1=0

We add all the numbers together, and all the variables

2X^2+22X-1=0

a = 2; b = 22; c = -1;
Δ = b2-4ac
Δ = 222-4·2·(-1)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{123}}{2*2}=\frac{-22-2\sqrt{123}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{123}}{2*2}=\frac{-22+2\sqrt{123}}{4}
$