5x+x^2=104

Solution for 5x+x^2=104 equation:

5x+x^2=104

We move all terms to the left:

5x+x^2-(104)=0

a = 1; b = 5; c = -104;
Δ = b2-4ac
Δ = 52-4·1·(-104)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-21}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*1}=\frac{16}{2}
=8
$