22-2x(x=8)

Solution for 22-2x(x=8) equation:

22-2x(x=8)

We move all terms to the left:

22-2x(x-(8))=0

We multiply parentheses

-2x^2+16x+22=0

a = -2; b = 16; c = +22;
Δ = b2-4ac
Δ = 162-4·(-2)·22
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-12\sqrt{3}}{2*-2}=\frac{-16-12\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+12\sqrt{3}}{2*-2}=\frac{-16+12\sqrt{3}}{-4}
$