4=x^2+x-20

Solution for 4=x^2+x-20 equation:

4=x^2+x-20

We move all terms to the left:

4-(x^2+x-20)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-1x+24=0

a = -1; b = -1; c = +24;
Δ = b2-4ac
Δ = -12-4·(-1)·24
Δ = 97
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{97}}{2*-1}=\frac{1-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-1}=\frac{1+\sqrt{97}}{-2}
$