6x-19=(12x-5)-(2x+7)/2

Solution for 6x-19=(12x-5)-(2x+7)/2 equation:

6x-19=(12x-5)-(2x+7)/2

We move all terms to the left:

6x-19-((12x-5)-(2x+7)/2)=0

We multiply all the terms by the denominator


6x*2)-((12x-5)-(2x+7)-19*2)=0

We add all the numbers together, and all the variables

6x*2)-((12x-5)-(2x+7)=0

Wy multiply elements

12x^2-(2x+7)=0

We get rid of parentheses

12x^2-2x-7=0

a = 12; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·12·(-7)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{85}}{2*12}=\frac{2-2\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{85}}{2*12}=\frac{2+2\sqrt{85}}{24}
$