0=-2x^2+92x-84

Solution for 0=-2x^2+92x-84 equation:

0=-2x^2+92x-84

We move all terms to the left:

0-(-2x^2+92x-84)=0

We add all the numbers together, and all the variables

-(-2x^2+92x-84)=0

We get rid of parentheses

2x^2-92x+84=0

a = 2; b = -92; c = +84;
Δ = b2-4ac
Δ = -922-4·2·84
Δ = 7792
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:

$\sqrt{\Delta}=\sqrt{7792}=\sqrt{16*487}=\sqrt{16}*\sqrt{487}=4\sqrt{487}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{487}}{2*2}=\frac{92-4\sqrt{487}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{487}}{2*2}=\frac{92+4\sqrt{487}}{4}
$