4x+x^2=150

Solution for 4x+x^2=150 equation:

4x+x^2=150

We move all terms to the left:

4x+x^2-(150)=0

a = 1; b = 4; c = -150;
Δ = b2-4ac
Δ = 42-4·1·(-150)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{154}}{2*1}=\frac{-4-2\sqrt{154}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{154}}{2*1}=\frac{-4+2\sqrt{154}}{2}
$