3a^2+4a^2=400

Solution for 3a^2+4a^2=400 equation:

3a^2+4a^2=400

We move all terms to the left:

3a^2+4a^2-(400)=0

We add all the numbers together, and all the variables

7a^2-400=0

a = 7; b = 0; c = -400;
Δ = b2-4ac
Δ = 02-4·7·(-400)
Δ = 11200
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:

$\sqrt{\Delta}=\sqrt{11200}=\sqrt{1600*7}=\sqrt{1600}*\sqrt{7}=40\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{7}}{2*7}=\frac{0-40\sqrt{7}}{14}
=-\frac{40\sqrt{7}}{14}
=-\frac{20\sqrt{7}}{7}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{7}}{2*7}=\frac{0+40\sqrt{7}}{14}
=\frac{40\sqrt{7}}{14}
=\frac{20\sqrt{7}}{7}
$