x/4-5=-x2

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

x/4-5=-x2

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(-1x^2)+x/4-5=0

We get rid of parentheses

1x^2+x/4-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

1x^2*4+x-20=0

Wy multiply elements

4x^2+x-20=0

a = 4; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·4·(-20)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{321}}{2*4}=\frac{-1-\sqrt{321}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{321}}{2*4}=\frac{-1+\sqrt{321}}{8}
$