x(x+4)=154

Solution for x(x+4)=154 equation:

x(x+4)=154

We move all terms to the left:

x(x+4)-(154)=0

We multiply parentheses

x^2+4x-154=0

a = 1; b = 4; c = -154;
Δ = b2-4ac
Δ = 42-4·1·(-154)
Δ = 632
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:

$\sqrt{\Delta}=\sqrt{632}=\sqrt{4*158}=\sqrt{4}*\sqrt{158}=2\sqrt{158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{158}}{2*1}=\frac{-4-2\sqrt{158}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{158}}{2*1}=\frac{-4+2\sqrt{158}}{2}
$