0=5x^2-22x+6

Solution for 0=5x^2-22x+6 equation:

0=5x^2-22x+6

We move all terms to the left:

0-(5x^2-22x+6)=0

We add all the numbers together, and all the variables

-(5x^2-22x+6)=0

We get rid of parentheses

-5x^2+22x-6=0

a = -5; b = 22; c = -6;
Δ = b2-4ac
Δ = 222-4·(-5)·(-6)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{91}}{2*-5}=\frac{-22-2\sqrt{91}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{91}}{2*-5}=\frac{-22+2\sqrt{91}}{-10}
$