x+19=133/2x+19=133/2x-19=133x+19=133/2

Solution for x+19=133/2x+19=133/2x-19=133x+19=133/2 equation:

x+19=133/2x+19=133/2x-19=133x+19=133/2

We move all terms to the left:

x+19-(133/2x+19)=0


Domain of the equation: 2x+19)!=0

x∈R


We get rid of parentheses

x-133/2x-19+19=0

We multiply all the terms by the denominator


x*2x-19*2x+19*2x-133=0

Wy multiply elements

2x^2-38x+38x-133=0

We add all the numbers together, and all the variables

2x^2-133=0

a = 2; b = 0; c = -133;
Δ = b2-4ac
Δ = 02-4·2·(-133)
Δ = 1064
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:

$\sqrt{\Delta}=\sqrt{1064}=\sqrt{4*266}=\sqrt{4}*\sqrt{266}=2\sqrt{266}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{266}}{2*2}=\frac{0-2\sqrt{266}}{4}
=-\frac{2\sqrt{266}}{4}
=-\frac{\sqrt{266}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{266}}{2*2}=\frac{0+2\sqrt{266}}{4}
=\frac{2\sqrt{266}}{4}
=\frac{\sqrt{266}}{2}
$