-20x^2-50x+200=30x-10

Solution for -20x^2-50x+200=30x-10 equation:

-20x^2-50x+200=30x-10

We move all terms to the left:

-20x^2-50x+200-(30x-10)=0

We get rid of parentheses

-20x^2-50x-30x+10+200=0

We add all the numbers together, and all the variables

-20x^2-80x+210=0

a = -20; b = -80; c = +210;
Δ = b2-4ac
Δ = -802-4·(-20)·210
Δ = 23200
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:

$\sqrt{\Delta}=\sqrt{23200}=\sqrt{400*58}=\sqrt{400}*\sqrt{58}=20\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{58}}{2*-20}=\frac{80-20\sqrt{58}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{58}}{2*-20}=\frac{80+20\sqrt{58}}{-40}
$