2x^2+5x^2=120

Solution for 2x^2+5x^2=120 equation:

2x^2+5x^2=120

We move all terms to the left:

2x^2+5x^2-(120)=0

We add all the numbers together, and all the variables

7x^2-120=0

a = 7; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·7·(-120)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*7}=\frac{0-4\sqrt{210}}{14}
=-\frac{4\sqrt{210}}{14}
=-\frac{2\sqrt{210}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*7}=\frac{0+4\sqrt{210}}{14}
=\frac{4\sqrt{210}}{14}
=\frac{2\sqrt{210}}{7}
$