x=-4x^2+16x-11

Solution for x=-4x^2+16x-11 equation:

x=-4x^2+16x-11

We move all terms to the left:

x-(-4x^2+16x-11)=0

We get rid of parentheses

4x^2-16x+x+11=0

We add all the numbers together, and all the variables

4x^2-15x+11=0

a = 4; b = -15; c = +11;
Δ = b2-4ac
Δ = -152-4·4·11
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-7}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+7}{2*4}=\frac{22}{8}
=2+3/4
$