10=-3x2+240x-800

Solution for 10=-3x2+240x-800 equation:

10=-3x^2+240x-800

We move all terms to the left:

10-(-3x^2+240x-800)=0

We get rid of parentheses

3x^2-240x+800+10=0

We add all the numbers together, and all the variables

3x^2-240x+810=0

a = 3; b = -240; c = +810;
Δ = b2-4ac
Δ = -2402-4·3·810
Δ = 47880
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:

$\sqrt{\Delta}=\sqrt{47880}=\sqrt{36*1330}=\sqrt{36}*\sqrt{1330}=6\sqrt{1330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-6\sqrt{1330}}{2*3}=\frac{240-6\sqrt{1330}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+6\sqrt{1330}}{2*3}=\frac{240+6\sqrt{1330}}{6}
$