12a^2+13a^2=300

Solution for 12a^2+13a^2=300 equation:

12a^2+13a^2=300

We move all terms to the left:

12a^2+13a^2-(300)=0

We add all the numbers together, and all the variables

25a^2-300=0

a = 25; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·25·(-300)
Δ = 30000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{30000}=\sqrt{10000*3}=\sqrt{10000}*\sqrt{3}=100\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{3}}{2*25}=\frac{0-100\sqrt{3}}{50}
=-\frac{100\sqrt{3}}{50}
=-2\sqrt{3}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{3}}{2*25}=\frac{0+100\sqrt{3}}{50}
=\frac{100\sqrt{3}}{50}
=2\sqrt{3}
$