x2+5x=900

Solution for x2+5x=900 equation:

x2+5x=900

We move all terms to the left:

x2+5x-(900)=0

We add all the numbers together, and all the variables

x^2+5x-900=0

a = 1; b = 5; c = -900;
Δ = b2-4ac
Δ = 52-4·1·(-900)
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{145}}{2*1}=\frac{-5-5\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{145}}{2*1}=\frac{-5+5\sqrt{145}}{2}
$