2x+100x+x^2=180

Solution for 2x+100x+x^2=180 equation:

2x+100x+x^2=180

We move all terms to the left:

2x+100x+x^2-(180)=0

We add all the numbers together, and all the variables

x^2+102x-180=0

a = 1; b = 102; c = -180;
Δ = b2-4ac
Δ = 1022-4·1·(-180)
Δ = 11124
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:

$\sqrt{\Delta}=\sqrt{11124}=\sqrt{36*309}=\sqrt{36}*\sqrt{309}=6\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{309}}{2*1}=\frac{-102-6\sqrt{309}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{309}}{2*1}=\frac{-102+6\sqrt{309}}{2}
$