4x(x-6)+2=6x-2

Solution for 4x(x-6)+2=6x-2 equation:

4x(x-6)+2=6x-2

We move all terms to the left:

4x(x-6)+2-(6x-2)=0

We multiply parentheses

4x^2-24x-(6x-2)+2=0

We get rid of parentheses

4x^2-24x-6x+2+2=0

We add all the numbers together, and all the variables

4x^2-30x+4=0

a = 4; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·4·4
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{209}}{2*4}=\frac{30-2\sqrt{209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{209}}{2*4}=\frac{30+2\sqrt{209}}{8}
$