3x^2+4x^2=50^2

Solution for 3x^2+4x^2=50^2 equation:

3x^2+4x^2=50^2

We move all terms to the left:

3x^2+4x^2-(50^2)=0

We add all the numbers together, and all the variables

7x^2-2500=0

a = 7; b = 0; c = -2500;
Δ = b2-4ac
Δ = 02-4·7·(-2500)
Δ = 70000
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:

$\sqrt{\Delta}=\sqrt{70000}=\sqrt{10000*7}=\sqrt{10000}*\sqrt{7}=100\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{7}}{2*7}=\frac{0-100\sqrt{7}}{14}
=-\frac{100\sqrt{7}}{14}
=-\frac{50\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{7}}{2*7}=\frac{0+100\sqrt{7}}{14}
=\frac{100\sqrt{7}}{14}
=\frac{50\sqrt{7}}{7}
$