2x^2+5x^2=105

Solution for 2x^2+5x^2=105 equation:

2x^2+5x^2=105

We move all terms to the left:

2x^2+5x^2-(105)=0

We add all the numbers together, and all the variables

7x^2-105=0

a = 7; b = 0; c = -105;
Δ = b2-4ac
Δ = 02-4·7·(-105)
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{15}}{2*7}=\frac{0-14\sqrt{15}}{14}
=-\frac{14\sqrt{15}}{14}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{15}}{2*7}=\frac{0+14\sqrt{15}}{14}
=\frac{14\sqrt{15}}{14}
=\sqrt{15}
$