2x^2+3x^2=2018

Solution for 2x^2+3x^2=2018 equation:

2x^2+3x^2=2018

We move all terms to the left:

2x^2+3x^2-(2018)=0

We add all the numbers together, and all the variables

5x^2-2018=0

a = 5; b = 0; c = -2018;
Δ = b2-4ac
Δ = 02-4·5·(-2018)
Δ = 40360
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:

$\sqrt{\Delta}=\sqrt{40360}=\sqrt{4*10090}=\sqrt{4}*\sqrt{10090}=2\sqrt{10090}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10090}}{2*5}=\frac{0-2\sqrt{10090}}{10}
=-\frac{2\sqrt{10090}}{10}
=-\frac{\sqrt{10090}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10090}}{2*5}=\frac{0+2\sqrt{10090}}{10}
=\frac{2\sqrt{10090}}{10}
=\frac{\sqrt{10090}}{5}
$