4x+x^2=146

Solution for 4x+x^2=146 equation:

4x+x^2=146

We move all terms to the left:

4x+x^2-(146)=0

a = 1; b = 4; c = -146;
Δ = b2-4ac
Δ = 42-4·1·(-146)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10\sqrt{6}}{2*1}=\frac{-4-10\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10\sqrt{6}}{2*1}=\frac{-4+10\sqrt{6}}{2}
$