x^2+30x+225=289

Solution for x^2+30x+225=289 equation:

x^2+30x+225=289

We move all terms to the left:

x^2+30x+225-(289)=0

We add all the numbers together, and all the variables

x^2+30x-64=0

a = 1; b = 30; c = -64;
Δ = b2-4ac
Δ = 302-4·1·(-64)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-34}{2*1}=\frac{-64}{2}
=-32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+34}{2*1}=\frac{4}{2}
=2
$