X^2+x=24.5

Solution for X^2+x=24.5 equation:

X^2+X=24.5

We move all terms to the left:

X^2+X-(24.5)=0

We add all the numbers together, and all the variables

X^2+X-24.5=0

a = 1; b = 1; c = -24.5;
Δ = b2-4ac
Δ = 12-4·1·(-24.5)
Δ = 99
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:

$\sqrt{\Delta}=\sqrt{99}=\sqrt{9*11}=\sqrt{9}*\sqrt{11}=3\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{11}}{2*1}=\frac{-1-3\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{11}}{2*1}=\frac{-1+3\sqrt{11}}{2}
$