4x^2+3x^2=65^2

Solution for 4x^2+3x^2=65^2 equation:

4x^2+3x^2=65^2

We move all terms to the left:

4x^2+3x^2-(65^2)=0

We add all the numbers together, and all the variables

7x^2-4225=0

a = 7; b = 0; c = -4225;
Δ = b2-4ac
Δ = 02-4·7·(-4225)
Δ = 118300
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:

$\sqrt{\Delta}=\sqrt{118300}=\sqrt{16900*7}=\sqrt{16900}*\sqrt{7}=130\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-130\sqrt{7}}{2*7}=\frac{0-130\sqrt{7}}{14}
=-\frac{130\sqrt{7}}{14}
=-\frac{65\sqrt{7}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+130\sqrt{7}}{2*7}=\frac{0+130\sqrt{7}}{14}
=\frac{130\sqrt{7}}{14}
=\frac{65\sqrt{7}}{7}
$