x^2+5x=300^2

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

x^2+5x=300^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2+5x-90000=0

a = 1; b = 5; c = -90000;
Δ = b2-4ac
Δ = 52-4·1·(-90000)
Δ = 360025
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:

$\sqrt{\Delta}=\sqrt{360025}=\sqrt{25*14401}=\sqrt{25}*\sqrt{14401}=5\sqrt{14401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{14401}}{2*1}=\frac{-5-5\sqrt{14401}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{14401}}{2*1}=\frac{-5+5\sqrt{14401}}{2}
$