5x+x^2=30

Solution for 5x+x^2=30 equation:

5x+x^2=30

We move all terms to the left:

5x+x^2-(30)=0

a = 1; b = 5; c = -30;
Δ = b2-4ac
Δ = 52-4·1·(-30)
Δ = 145
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{145}}{2*1}=\frac{-5-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{145}}{2*1}=\frac{-5+\sqrt{145}}{2}
$