0.25x^2=24+x

Solution for 0.25x^2=24+x equation:

0.25x^2=24+x

We move all terms to the left:

0.25x^2-(24+x)=0

We add all the numbers together, and all the variables

0.25x^2-(x+24)=0

We get rid of parentheses

0.25x^2-x-24=0

We add all the numbers together, and all the variables

0.25x^2-1x-24=0

a = 0.25; b = -1; c = -24;
Δ = b2-4ac
Δ = -12-4·0.25·(-24)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*0.25}=\frac{-4}{0.5}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*0.25}=\frac{6}{0.5}
=12
$