x=-2x^2+34x-107

Solution for x=-2x^2+34x-107 equation:

x=-2x^2+34x-107

We move all terms to the left:

x-(-2x^2+34x-107)=0

We get rid of parentheses

2x^2-34x+x+107=0

We add all the numbers together, and all the variables

2x^2-33x+107=0

a = 2; b = -33; c = +107;
Δ = b2-4ac
Δ = -332-4·2·107
Δ = 233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-\sqrt{233}}{2*2}=\frac{33-\sqrt{233}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+\sqrt{233}}{2*2}=\frac{33+\sqrt{233}}{4}
$