0=5x^2+33x-14

Solution for 0=5x^2+33x-14 equation:

0=5x^2+33x-14

We move all terms to the left:

0-(5x^2+33x-14)=0

We add all the numbers together, and all the variables

-(5x^2+33x-14)=0

We get rid of parentheses

-5x^2-33x+14=0

a = -5; b = -33; c = +14;
Δ = b2-4ac
Δ = -332-4·(-5)·14
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{-(-33)-37}{2*-5}=\frac{-4}{-10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+37}{2*-5}=\frac{70}{-10}
=-7
$