6x-19=(1/2)(12x-5-(2x+7

Solution for 6x-19=(1/2)(12x-5-(2x+7 equation:

6x-19=(1/2)(12x-5-(2x+7

We move all terms to the left:

6x-19-((1/2)(12x-5-(2x+7)=0


Domain of the equation: 2)(12x-5-(2x+7)-19!=0

We move all terms containing x to the left, all other terms to the right

2)(12x-(2x+7)!=24

x∈R


We add all the numbers together, and all the variables

6x-((+1/2)(12x-5-(2x+7)-19=0

We multiply all the terms by the denominator


6x*2)(12x-(2x+7)-5-19-((+1=0

We add all the numbers together, and all the variables

6x*2)(12x-(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}
$