6(2-7x)+x(7x-2=0)

Solution for 6(2-7x)+x(7x-2=0) equation:

6(2-7x)+x(7x-2=0)

We move all terms to the left:

6(2-7x)+x(7x-2-(0))=0

We add all the numbers together, and all the variables

6(-7x+2)+x(7x-2)=0

We multiply parentheses

7x^2-42x-2x+12=0

We add all the numbers together, and all the variables

7x^2-44x+12=0

a = 7; b = -44; c = +12;
Δ = b2-4ac
Δ = -442-4·7·12
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-40}{2*7}=\frac{4}{14}
=2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+40}{2*7}=\frac{84}{14}
=6
$