0=7x^2-24x+6

Solution for 0=7x^2-24x+6 equation:

0=7x^2-24x+6

We move all terms to the left:

0-(7x^2-24x+6)=0

We add all the numbers together, and all the variables

-(7x^2-24x+6)=0

We get rid of parentheses

-7x^2+24x-6=0

a = -7; b = 24; c = -6;
Δ = b2-4ac
Δ = 242-4·(-7)·(-6)
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{102}}{2*-7}=\frac{-24-2\sqrt{102}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{102}}{2*-7}=\frac{-24+2\sqrt{102}}{-14}
$