0=5x^2-6x-192

Solution for 0=5x^2-6x-192 equation:

0=5x^2-6x-192

We move all terms to the left:

0-(5x^2-6x-192)=0

We add all the numbers together, and all the variables

-(5x^2-6x-192)=0

We get rid of parentheses

-5x^2+6x+192=0

a = -5; b = 6; c = +192;
Δ = b2-4ac
Δ = 62-4·(-5)·192
Δ = 3876
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:

$\sqrt{\Delta}=\sqrt{3876}=\sqrt{4*969}=\sqrt{4}*\sqrt{969}=2\sqrt{969}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{969}}{2*-5}=\frac{-6-2\sqrt{969}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{969}}{2*-5}=\frac{-6+2\sqrt{969}}{-10}
$