7=22-16x+4x^2

Solution for 7=22-16x+4x^2 equation:

7=22-16x+4x^2

We move all terms to the left:

7-(22-16x+4x^2)=0

We get rid of parentheses

-4x^2+16x-22+7=0

We add all the numbers together, and all the variables

-4x^2+16x-15=0

a = -4; b = 16; c = -15;
Δ = b2-4ac
Δ = 162-4·(-4)·(-15)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4}{2*-4}=\frac{-12}{-8}
=1+1/2
$