2x(22-10x)=-2

Solution for 2x(22-10x)=-2 equation:

2x(22-10x)=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x(-10x+22)-(-2)=0

We add all the numbers together, and all the variables

2x(-10x+22)+2=0

We multiply parentheses

-20x^2+44x+2=0

a = -20; b = 44; c = +2;
Δ = b2-4ac
Δ = 442-4·(-20)·2
Δ = 2096
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:

$\sqrt{\Delta}=\sqrt{2096}=\sqrt{16*131}=\sqrt{16}*\sqrt{131}=4\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{131}}{2*-20}=\frac{-44-4\sqrt{131}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{131}}{2*-20}=\frac{-44+4\sqrt{131}}{-40}
$