100x-5x^2=30x^2

Solution for 100x-5x^2=30x^2 equation:

100x-5x^2=30x^2

We move all terms to the left:

100x-5x^2-(30x^2)=0

determiningTheFunctionDomain
-5x^2-30x^2+100x=0

We add all the numbers together, and all the variables

-35x^2+100x=0

a = -35; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-35)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-35}=\frac{-200}{-70}
=2+6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-35}=\frac{0}{-70}
=0
$