2=-4x^2+16x

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

2=-4x^2+16x

We move all terms to the left:

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

We get rid of parentheses

4x^2-16x+2=0

a = 4; b = -16; c = +2;
Δ = b2-4ac
Δ = -162-4·4·2
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{14}}{2*4}=\frac{16-4\sqrt{14}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{14}}{2*4}=\frac{16+4\sqrt{14}}{8}
$