100x-0.25x^2=2500+16x-0.05x^2

Solution for 100x-0.25x^2=2500+16x-0.05x^2 equation:

100x-0.25x^2=2500+16x-0.05x^2

We move all terms to the left:

100x-0.25x^2-(2500+16x-0.05x^2)=0

We get rid of parentheses

-0.25x^2+0.05x^2-16x+100x-2500=0

We add all the numbers together, and all the variables

-0.2x^2+84x-2500=0

a = -0.2; b = 84; c = -2500;
Δ = b2-4ac
Δ = 842-4·(-0.2)·(-2500)
Δ = 5056
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:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-8\sqrt{79}}{2*-0.2}=\frac{-84-8\sqrt{79}}{-0.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+8\sqrt{79}}{2*-0.2}=\frac{-84+8\sqrt{79}}{-0.4}
$