99x^2-200x=100

Solution for 99x^2-200x=100 equation:

99x^2-200x=100

We move all terms to the left:

99x^2-200x-(100)=0

a = 99; b = -200; c = -100;
Δ = b2-4ac
Δ = -2002-4·99·(-100)
Δ = 79600
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:

$\sqrt{\Delta}=\sqrt{79600}=\sqrt{400*199}=\sqrt{400}*\sqrt{199}=20\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-20\sqrt{199}}{2*99}=\frac{200-20\sqrt{199}}{198}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+20\sqrt{199}}{2*99}=\frac{200+20\sqrt{199}}{198}
$