X^2+35x+300=900

Solution for X^2+35x+300=900 equation:

X^2+35X+300=900

We move all terms to the left:

X^2+35X+300-(900)=0

We add all the numbers together, and all the variables

X^2+35X-600=0

a = 1; b = 35; c = -600;
Δ = b2-4ac
Δ = 352-4·1·(-600)
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{-(35)-5\sqrt{145}}{2*1}=\frac{-35-5\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{145}}{2*1}=\frac{-35+5\sqrt{145}}{2}
$