2x2+3x2=1024

Solution for 2x2+3x2=1024 equation:

2x^2+3x^2=1024

We move all terms to the left:

2x^2+3x^2-(1024)=0

We add all the numbers together, and all the variables

5x^2-1024=0

a = 5; b = 0; c = -1024;
Δ = b2-4ac
Δ = 02-4·5·(-1024)
Δ = 20480
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:

$\sqrt{\Delta}=\sqrt{20480}=\sqrt{4096*5}=\sqrt{4096}*\sqrt{5}=64\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{5}}{2*5}=\frac{0-64\sqrt{5}}{10}
=-\frac{64\sqrt{5}}{10}
=-\frac{32\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{5}}{2*5}=\frac{0+64\sqrt{5}}{10}
=\frac{64\sqrt{5}}{10}
=\frac{32\sqrt{5}}{5}
$