0=5x+x^2-47.5

Solution for 0=5x+x^2-47.5 equation:

0=5x+x^2-47.5

We move all terms to the left:

0-(5x+x^2-47.5)=0

We add all the numbers together, and all the variables

-(5x+x^2-47.5)=0

We get rid of parentheses

-x^2-5x+47.5=0

We add all the numbers together, and all the variables

-1x^2-5x+47.5=0

a = -1; b = -5; c = +47.5;
Δ = b2-4ac
Δ = -52-4·(-1)·47.5
Δ = 215
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{-(-5)-\sqrt{215}}{2*-1}=\frac{5-\sqrt{215}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{215}}{2*-1}=\frac{5+\sqrt{215}}{-2}
$