0=20x^2-33x-23

Solution for 0=20x^2-33x-23 equation:

0=20x^2-33x-23

We move all terms to the left:

0-(20x^2-33x-23)=0

We add all the numbers together, and all the variables

-(20x^2-33x-23)=0

We get rid of parentheses

-20x^2+33x+23=0

a = -20; b = 33; c = +23;
Δ = b2-4ac
Δ = 332-4·(-20)·23
Δ = 2929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{2929}}{2*-20}=\frac{-33-\sqrt{2929}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{2929}}{2*-20}=\frac{-33+\sqrt{2929}}{-40}
$