x^2+3x^2+2x-120=0

Solution for x^2+3x^2+2x-120=0 equation:

x^2+3x^2+2x-120=0

We add all the numbers together, and all the variables

4x^2+2x-120=0

a = 4; b = 2; c = -120;
Δ = b2-4ac
Δ = 22-4·4·(-120)
Δ = 1924
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:

$\sqrt{\Delta}=\sqrt{1924}=\sqrt{4*481}=\sqrt{4}*\sqrt{481}=2\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{481}}{2*4}=\frac{-2-2\sqrt{481}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{481}}{2*4}=\frac{-2+2\sqrt{481}}{8}
$