x=-2x2+16x+40

Solution for x=-2x2+16x+40 equation:

x=-2x^2+16x+40

We move all terms to the left:

x-(-2x^2+16x+40)=0

We get rid of parentheses

2x^2-16x+x-40=0

We add all the numbers together, and all the variables

2x^2-15x-40=0

a = 2; b = -15; c = -40;
Δ = b2-4ac
Δ = -152-4·2·(-40)
Δ = 545
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{-(-15)-\sqrt{545}}{2*2}=\frac{15-\sqrt{545}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{545}}{2*2}=\frac{15+\sqrt{545}}{4}
$