x+30x2+x=180

Solution for x+30x2+x=180 equation:

x+30x^2+x=180

We move all terms to the left:

x+30x^2+x-(180)=0

We add all the numbers together, and all the variables

30x^2+2x-180=0

a = 30; b = 2; c = -180;
Δ = b2-4ac
Δ = 22-4·30·(-180)
Δ = 21604
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:

$\sqrt{\Delta}=\sqrt{21604}=\sqrt{4*5401}=\sqrt{4}*\sqrt{5401}=2\sqrt{5401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5401}}{2*30}=\frac{-2-2\sqrt{5401}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5401}}{2*30}=\frac{-2+2\sqrt{5401}}{60}
$