6x^2-14x=2x-8

Solution for 6x^2-14x=2x-8 equation:

6x^2-14x=2x-8

We move all terms to the left:

6x^2-14x-(2x-8)=0

We get rid of parentheses

6x^2-14x-2x+8=0

We add all the numbers together, and all the variables

6x^2-16x+8=0

a = 6; b = -16; c = +8;
Δ = b2-4ac
Δ = -162-4·6·8
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*6}=\frac{8}{12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*6}=\frac{24}{12}
=2
$