2x^2+3x^2=52

Solution for 2x^2+3x^2=52 equation:

2x^2+3x^2=52

We move all terms to the left:

2x^2+3x^2-(52)=0

We add all the numbers together, and all the variables

5x^2-52=0

a = 5; b = 0; c = -52;
Δ = b2-4ac
Δ = 02-4·5·(-52)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{65}}{2*5}=\frac{0-4\sqrt{65}}{10}
=-\frac{4\sqrt{65}}{10}
=-\frac{2\sqrt{65}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{65}}{2*5}=\frac{0+4\sqrt{65}}{10}
=\frac{4\sqrt{65}}{10}
=\frac{2\sqrt{65}}{5}
$