5+x*20=46+x^2

Solution for 5+x*20=46+x^2 equation:

5+x*20=46+x^2

We move all terms to the left:

5+x*20-(46+x^2)=0

Wy multiply elements

-(46+x^2)+20x+5=0

We get rid of parentheses

-x^2+20x-46+5=0

We add all the numbers together, and all the variables

-1x^2+20x-41=0

a = -1; b = 20; c = -41;
Δ = b2-4ac
Δ = 202-4·(-1)·(-41)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{59}}{2*-1}=\frac{-20-2\sqrt{59}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{59}}{2*-1}=\frac{-20+2\sqrt{59}}{-2}
$