-22=x-5x^2

Solution for -22=x-5x^2 equation:

-22=x-5x^2

We move all terms to the left:

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

We get rid of parentheses

5x^2-x-22=0

We add all the numbers together, and all the variables

5x^2-1x-22=0

a = 5; b = -1; c = -22;
Δ = b2-4ac
Δ = -12-4·5·(-22)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-21}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+21}{2*5}=\frac{22}{10}
=2+1/5
$