3x^2+2x-114=0

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

3x^2+2x-114=0

a = 3; b = 2; c = -114;
Δ = b2-4ac
Δ = 22-4·3·(-114)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14\sqrt{7}}{2*3}=\frac{-2-14\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14\sqrt{7}}{2*3}=\frac{-2+14\sqrt{7}}{6}
$