300x=45x^2

Solution for 300x=45x^2 equation:

300x=45x^2

We move all terms to the left:

300x-(45x^2)=0

determiningTheFunctionDomain
-45x^2+300x=0

a = -45; b = 300; c = 0;
Δ = b2-4ac
Δ = 3002-4·(-45)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-300}{2*-45}=\frac{-600}{-90}
=6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+300}{2*-45}=\frac{0}{-90}
=0
$