0=7x2-40x-12

Solution for 0=7x2-40x-12 equation:

0=7x^2-40x-12

We move all terms to the left:

0-(7x^2-40x-12)=0

We add all the numbers together, and all the variables

-(7x^2-40x-12)=0

We get rid of parentheses

-7x^2+40x+12=0

a = -7; b = 40; c = +12;
Δ = b2-4ac
Δ = 402-4·(-7)·12
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-44}{2*-7}=\frac{-84}{-14}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+44}{2*-7}=\frac{4}{-14}
=-2/7
$