66=2x^2-14x+78

Solution for 66=2x^2-14x+78 equation:

66=2x^2-14x+78

We move all terms to the left:

66-(2x^2-14x+78)=0

We get rid of parentheses

-2x^2+14x-78+66=0

We add all the numbers together, and all the variables

-2x^2+14x-12=0

a = -2; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-2)·(-12)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-2}=\frac{-4}{-4}
=1
$