x=-2x^2+8x+45

Solution for x=-2x^2+8x+45 equation:

x=-2x^2+8x+45

We move all terms to the left:

x-(-2x^2+8x+45)=0

We get rid of parentheses

2x^2-8x+x-45=0

We add all the numbers together, and all the variables

2x^2-7x-45=0

a = 2; b = -7; c = -45;
Δ = b2-4ac
Δ = -72-4·2·(-45)
Δ = 409
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{-(-7)-\sqrt{409}}{2*2}=\frac{7-\sqrt{409}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{409}}{2*2}=\frac{7+\sqrt{409}}{4}
$