0=48x^2-4x-80

Solution for 0=48x^2-4x-80 equation:

0=48x^2-4x-80

We move all terms to the left:

0-(48x^2-4x-80)=0

We add all the numbers together, and all the variables

-(48x^2-4x-80)=0

We get rid of parentheses

-48x^2+4x+80=0

a = -48; b = 4; c = +80;
Δ = b2-4ac
Δ = 42-4·(-48)·80
Δ = 15376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15376}=124$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-124}{2*-48}=\frac{-128}{-96}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+124}{2*-48}=\frac{120}{-96}
=-1+1/4
$