48.75=x^2+x

Solution for 48.75=x^2+x equation:

48.75=x^2+x

We move all terms to the left:

48.75-(x^2+x)=0

We get rid of parentheses

-x^2-x+48.75=0

We add all the numbers together, and all the variables

-1x^2-1x+48.75=0

a = -1; b = -1; c = +48.75;
Δ = b2-4ac
Δ = -12-4·(-1)·48.75
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-14}{2*-1}=\frac{-13}{-2}
=6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+14}{2*-1}=\frac{15}{-2}
=-7+1/2
$