6x-20=2x^2-12x+16

Solution for 6x-20=2x^2-12x+16 equation:

6x-20=2x^2-12x+16

We move all terms to the left:

6x-20-(2x^2-12x+16)=0

We get rid of parentheses

-2x^2+6x+12x-16-20=0

We add all the numbers together, and all the variables

-2x^2+18x-36=0

a = -2; b = 18; c = -36;
Δ = b2-4ac
Δ = 182-4·(-2)·(-36)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*-2}=\frac{-12}{-4}
=+3
$