2x+x*x=154

Solution for 2x+x*x=154 equation:

2x+x*x=154

We move all terms to the left:

2x+x*x-(154)=0

Wy multiply elements

x^2+2x-154=0

a = 1; b = 2; c = -154;
Δ = b2-4ac
Δ = 22-4·1·(-154)
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{155}}{2*1}=\frac{-2-2\sqrt{155}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{155}}{2*1}=\frac{-2+2\sqrt{155}}{2}
$