6x^2=8x-2

Solution for 6x^2=8x-2 equation:

6x^2=8x-2

We move all terms to the left:

6x^2-(8x-2)=0

We get rid of parentheses

6x^2-8x+2=0

a = 6; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·6·2
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*6}=\frac{4}{12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*6}=\frac{12}{12}
=1
$