22=6x^2-10x-2

Solution for 22=6x^2-10x-2 equation:

22=6x^2-10x-2

We move all terms to the left:

22-(6x^2-10x-2)=0

We get rid of parentheses

-6x^2+10x+2+22=0

We add all the numbers together, and all the variables

-6x^2+10x+24=0

a = -6; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·(-6)·24
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-26}{2*-6}=\frac{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+26}{2*-6}=\frac{16}{-12}
=-1+1/3
$