100x-25x^2=3

Solution for 100x-25x^2=3 equation:

100x-25x^2=3

We move all terms to the left:

100x-25x^2-(3)=0

a = -25; b = 100; c = -3;
Δ = b2-4ac
Δ = 1002-4·(-25)·(-3)
Δ = 9700
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:

$\sqrt{\Delta}=\sqrt{9700}=\sqrt{100*97}=\sqrt{100}*\sqrt{97}=10\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-10\sqrt{97}}{2*-25}=\frac{-100-10\sqrt{97}}{-50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+10\sqrt{97}}{2*-25}=\frac{-100+10\sqrt{97}}{-50}
$