2400-10x=6x^2-30x+400

Solution for 2400-10x=6x^2-30x+400 equation:

2400-10x=6x^2-30x+400

We move all terms to the left:

2400-10x-(6x^2-30x+400)=0

We get rid of parentheses

-6x^2-10x+30x-400+2400=0

We add all the numbers together, and all the variables

-6x^2+20x+2000=0

a = -6; b = 20; c = +2000;
Δ = b2-4ac
Δ = 202-4·(-6)·2000
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-220}{2*-6}=\frac{-240}{-12}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+220}{2*-6}=\frac{200}{-12}
=-16+2/3
$