-20x^2+200x+4000=4300

Solution for -20x^2+200x+4000=4300 equation:

-20x^2+200x+4000=4300

We move all terms to the left:

-20x^2+200x+4000-(4300)=0

We add all the numbers together, and all the variables

-20x^2+200x-300=0

a = -20; b = 200; c = -300;
Δ = b2-4ac
Δ = 2002-4·(-20)·(-300)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-40\sqrt{10}}{2*-20}=\frac{-200-40\sqrt{10}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+40\sqrt{10}}{2*-20}=\frac{-200+40\sqrt{10}}{-40}
$