18x^2-x-120=0

Solution for 18x^2-x-120=0 equation:

18x^2-x-120=0

We add all the numbers together, and all the variables

18x^2-1x-120=0

a = 18; b = -1; c = -120;
Δ = b2-4ac
Δ = -12-4·18·(-120)
Δ = 8641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{8641}}{2*18}=\frac{1-\sqrt{8641}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{8641}}{2*18}=\frac{1+\sqrt{8641}}{36}
$