4-x2/4=5x

Solution for 4-x2/4=5x equation:

4-x2/4=5x

We move all terms to the left:

4-x2/4-(5x)=0

We add all the numbers together, and all the variables

-5x-x2/4+4=0

We multiply all the terms by the denominator


-5x*4-x2+4*4=0

We add all the numbers together, and all the variables

-1x^2-5x*4+16=0

Wy multiply elements

-1x^2-20x+16=0

a = -1; b = -20; c = +16;
Δ = b2-4ac
Δ = -202-4·(-1)·16
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{29}}{2*-1}=\frac{20-4\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{29}}{2*-1}=\frac{20+4\sqrt{29}}{-2}
$