x(7-6x)=2

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

x(7-6x)=2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-6x^2+7x-2=0

a = -6; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-6)·(-2)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-1}{2*-6}=\frac{-8}{-12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-6}=\frac{-6}{-12}
=1/2
$