(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+31)=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+31)-26=0

We multiply parentheses

19x^2-(6x+31)-26=0

We get rid of parentheses

19x^2-6x-31-26=0

We add all the numbers together, and all the variables

19x^2-6x-57=0

a = 19; b = -6; c = -57;
Δ = b2-4ac
Δ = -62-4·19·(-57)
Δ = 4368
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:

$\sqrt{\Delta}=\sqrt{4368}=\sqrt{16*273}=\sqrt{16}*\sqrt{273}=4\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{273}}{2*19}=\frac{6-4\sqrt{273}}{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{273}}{2*19}=\frac{6+4\sqrt{273}}{38}
$