x^2/4-5x+x^2=16

Solution for x^2/4-5x+x^2=16 equation:

x^2/4-5x+x^2=16

We move all terms to the left:

x^2/4-5x+x^2-(16)=0

We add all the numbers together, and all the variables

x^2+x^2/4-5x-16=0

We multiply all the terms by the denominator


x^2+x^2*4-5x*4-16*4=0

We add all the numbers together, and all the variables

x^2+x^2*4-5x*4-64=0

Wy multiply elements

x^2+4x^2-20x-64=0

We add all the numbers together, and all the variables

5x^2-20x-64=0

a = 5; b = -20; c = -64;
Δ = b2-4ac
Δ = -202-4·5·(-64)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{105}}{2*5}=\frac{20-4\sqrt{105}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{105}}{2*5}=\frac{20+4\sqrt{105}}{10}
$