0=12x^2-13x-35

Solution for 0=12x^2-13x-35 equation:

0=12x^2-13x-35

We move all terms to the left:

0-(12x^2-13x-35)=0

We add all the numbers together, and all the variables

-(12x^2-13x-35)=0

We get rid of parentheses

-12x^2+13x+35=0

a = -12; b = 13; c = +35;
Δ = b2-4ac
Δ = 132-4·(-12)·35
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-43}{2*-12}=\frac{-56}{-24}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+43}{2*-12}=\frac{30}{-24}
=-1+1/4
$