2x(x-3)=200

Solution for 2x(x-3)=200 equation:

2x(x-3)=200

We move all terms to the left:

2x(x-3)-(200)=0

We multiply parentheses

2x^2-6x-200=0

a = 2; b = -6; c = -200;
Δ = b2-4ac
Δ = -62-4·2·(-200)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{409}}{2*2}=\frac{6-2\sqrt{409}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{409}}{2*2}=\frac{6+2\sqrt{409}}{4}
$