4x^2+2x^2=84

Solution for 4x^2+2x^2=84 equation:

4x^2+2x^2=84

We move all terms to the left:

4x^2+2x^2-(84)=0

We add all the numbers together, and all the variables

6x^2-84=0

a = 6; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·6·(-84)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*6}=\frac{0-12\sqrt{14}}{12}
=-\frac{12\sqrt{14}}{12}
=-\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*6}=\frac{0+12\sqrt{14}}{12}
=\frac{12\sqrt{14}}{12}
=\sqrt{14}
$