0=-10x^2+400x-310

Solution for 0=-10x^2+400x-310 equation:

0=-10x^2+400x-310

We move all terms to the left:

0-(-10x^2+400x-310)=0

We add all the numbers together, and all the variables

-(-10x^2+400x-310)=0

We get rid of parentheses

10x^2-400x+310=0

a = 10; b = -400; c = +310;
Δ = b2-4ac
Δ = -4002-4·10·310
Δ = 147600
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:

$\sqrt{\Delta}=\sqrt{147600}=\sqrt{3600*41}=\sqrt{3600}*\sqrt{41}=60\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-60\sqrt{41}}{2*10}=\frac{400-60\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+60\sqrt{41}}{2*10}=\frac{400+60\sqrt{41}}{20}
$