0=6x^2-7x-3

Solution for 0=6x^2-7x-3 equation:

0=6x^2-7x-3

We move all terms to the left:

0-(6x^2-7x-3)=0

We add all the numbers together, and all the variables

-(6x^2-7x-3)=0

We get rid of parentheses

-6x^2+7x+3=0

a = -6; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-6)·3
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-6}=\frac{4}{-12}
=-1/3
$