4x+x^2=73

Solution for 4x+x^2=73 equation:

4x+x^2=73

We move all terms to the left:

4x+x^2-(73)=0

a = 1; b = 4; c = -73;
Δ = b2-4ac
Δ = 42-4·1·(-73)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{77}}{2*1}=\frac{-4-2\sqrt{77}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{77}}{2*1}=\frac{-4+2\sqrt{77}}{2}
$