0=7x^2-2x-6

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

0=7x^2-2x-6

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

a = -7; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-7)·6
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{43}}{2*-7}=\frac{-2-2\sqrt{43}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{43}}{2*-7}=\frac{-2+2\sqrt{43}}{-14}
$