3x^2-x-114=0

Solution for 3x^2-x-114=0 equation:

3x^2-x-114=0

We add all the numbers together, and all the variables

3x^2-1x-114=0

a = 3; b = -1; c = -114;
Δ = b2-4ac
Δ = -12-4·3·(-114)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-37}{2*3}=\frac{-36}{6}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+37}{2*3}=\frac{38}{6}
=6+1/3
$