0=7x^2-22x+6

Solution for 0=7x^2-22x+6 equation:

0=7x^2-22x+6

We move all terms to the left:

0-(7x^2-22x+6)=0

We add all the numbers together, and all the variables

-(7x^2-22x+6)=0

We get rid of parentheses

-7x^2+22x-6=0

a = -7; b = 22; c = -6;
Δ = b2-4ac
Δ = 222-4·(-7)·(-6)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{79}}{2*-7}=\frac{-22-2\sqrt{79}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{79}}{2*-7}=\frac{-22+2\sqrt{79}}{-14}
$