(1/2)19x-26=6x=31

Solution for (1/2)19x-26=6x=31 equation:

(1/2)19x-26=6x=31

We move all terms to the left:

(1/2)19x-26-(6x)=0


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)19x-6x-26=0

We add all the numbers together, and all the variables

-6x+(+1/2)19x-26=0

We multiply parentheses

19x^2-6x-26=0

a = 19; b = -6; c = -26;
Δ = b2-4ac
Δ = -62-4·19·(-26)
Δ = 2012
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:

$\sqrt{\Delta}=\sqrt{2012}=\sqrt{4*503}=\sqrt{4}*\sqrt{503}=2\sqrt{503}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{503}}{2*19}=\frac{6-2\sqrt{503}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{503}}{2*19}=\frac{6+2\sqrt{503}}{38}
$