7x+x^2=24

Solution for 7x+x^2=24 equation:

7x+x^2=24

We move all terms to the left:

7x+x^2-(24)=0

a = 1; b = 7; c = -24;
Δ = b2-4ac
Δ = 72-4·1·(-24)
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{-(7)-\sqrt{145}}{2*1}=\frac{-7-\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*1}=\frac{-7+\sqrt{145}}{2}
$