X-19=1/2x+6

Solution for X-19=1/2x+6 equation:

X-19=1/2X+6

We move all terms to the left:

X-19-(1/2X+6)=0


Domain of the equation: 2X+6)!=0

X∈R


We get rid of parentheses

X-1/2X-6-19=0

We multiply all the terms by the denominator


X*2X-6*2X-19*2X-1=0

Wy multiply elements

2X^2-12X-38X-1=0

We add all the numbers together, and all the variables

2X^2-50X-1=0

a = 2; b = -50; c = -1;
Δ = b2-4ac
Δ = -502-4·2·(-1)
Δ = 2508
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:

$\sqrt{\Delta}=\sqrt{2508}=\sqrt{4*627}=\sqrt{4}*\sqrt{627}=2\sqrt{627}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{627}}{2*2}=\frac{50-2\sqrt{627}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{627}}{2*2}=\frac{50+2\sqrt{627}}{4}
$