300x+10000=5x^2+200x

Solution for 300x+10000=5x^2+200x equation:

300x+10000=5x^2+200x

We move all terms to the left:

300x+10000-(5x^2+200x)=0

We get rid of parentheses

-5x^2+300x-200x+10000=0

We add all the numbers together, and all the variables

-5x^2+100x+10000=0

a = -5; b = 100; c = +10000;
Δ = b2-4ac
Δ = 1002-4·(-5)·10000
Δ = 210000
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:

$\sqrt{\Delta}=\sqrt{210000}=\sqrt{10000*21}=\sqrt{10000}*\sqrt{21}=100\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{21}}{2*-5}=\frac{-100-100\sqrt{21}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{21}}{2*-5}=\frac{-100+100\sqrt{21}}{-10}
$