0=3x^2+8x-14

Solution for 0=3x^2+8x-14 equation:

0=3x^2+8x-14

We move all terms to the left:

0-(3x^2+8x-14)=0

We add all the numbers together, and all the variables

-(3x^2+8x-14)=0

We get rid of parentheses

-3x^2-8x+14=0

a = -3; b = -8; c = +14;
Δ = b2-4ac
Δ = -82-4·(-3)·14
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{58}}{2*-3}=\frac{8-2\sqrt{58}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{58}}{2*-3}=\frac{8+2\sqrt{58}}{-6}
$