2x^2-24x+80=1000

Solution for 2x^2-24x+80=1000 equation:

2x^2-24x+80=1000

We move all terms to the left:

2x^2-24x+80-(1000)=0

We add all the numbers together, and all the variables

2x^2-24x-920=0

a = 2; b = -24; c = -920;
Δ = b2-4ac
Δ = -242-4·2·(-920)
Δ = 7936
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:

$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{31}}{2*2}=\frac{24-16\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{31}}{2*2}=\frac{24+16\sqrt{31}}{4}
$