(119x2)+(x2)=360

Solution for (119x2)+(x2)=360 equation:

(119x^2)+(x2)=360

We move all terms to the left:

(119x^2)+(x2)-(360)=0

We add all the numbers together, and all the variables

120x^2-360=0

a = 120; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·120·(-360)
Δ = 172800
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:

$\sqrt{\Delta}=\sqrt{172800}=\sqrt{57600*3}=\sqrt{57600}*\sqrt{3}=240\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240\sqrt{3}}{2*120}=\frac{0-240\sqrt{3}}{240}
=-\frac{240\sqrt{3}}{240}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240\sqrt{3}}{2*120}=\frac{0+240\sqrt{3}}{240}
=\frac{240\sqrt{3}}{240}
=\sqrt{3}
$