3x^2+4x-113=0

Solution for 3x^2+4x-113=0 equation:

3x^2+4x-113=0

a = 3; b = 4; c = -113;
Δ = b2-4ac
Δ = 42-4·3·(-113)
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{-(4)-14\sqrt{7}}{2*3}=\frac{-4-14\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14\sqrt{7}}{2*3}=\frac{-4+14\sqrt{7}}{6}
$