25x^2+30x+225=12+225

Solution for 25x^2+30x+225=12+225 equation:

25x^2+30x+225=12+225

We move all terms to the left:

25x^2+30x+225-(12+225)=0

We add all the numbers together, and all the variables

25x^2+30x+225-237=0

We add all the numbers together, and all the variables

25x^2+30x-12=0

a = 25; b = 30; c = -12;
Δ = b2-4ac
Δ = 302-4·25·(-12)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{21}}{2*25}=\frac{-30-10\sqrt{21}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{21}}{2*25}=\frac{-30+10\sqrt{21}}{50}
$