x2+(x-4)2/16=1

Solution for x2+(x-4)2/16=1 equation:

x2+(x-4)2/16=1

We move all terms to the left:

x2+(x-4)2/16-(1)=0

We add all the numbers together, and all the variables

x^2+(x-4)2/16-1=0

We multiply all the terms by the denominator


x^2*16+(x-4)2-1*16=0

We add all the numbers together, and all the variables

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

We multiply parentheses

x^2*16+2x-8-16=0

Wy multiply elements

16x^2+2x-8-16=0

We add all the numbers together, and all the variables

16x^2+2x-24=0

a = 16; b = 2; c = -24;
Δ = b2-4ac
Δ = 22-4·16·(-24)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{385}}{2*16}=\frac{-2-2\sqrt{385}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{385}}{2*16}=\frac{-2+2\sqrt{385}}{32}
$