-x2+2-1+6x2-4x=22

Solution for -x2+2-1+6x2-4x=22 equation:

-x2+2-1+6x^2-4x=22

We move all terms to the left:

-x2+2-1+6x^2-4x-(22)=0

We add all the numbers together, and all the variables

5x^2-4x-21=0

a = 5; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·5·(-21)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{109}}{2*5}=\frac{4-2\sqrt{109}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{109}}{2*5}=\frac{4+2\sqrt{109}}{10}
$