2x^2+2+14x=180

Solution for 2x^2+2+14x=180 equation:

2x^2+2+14x=180

We move all terms to the left:

2x^2+2+14x-(180)=0

We add all the numbers together, and all the variables

2x^2+14x-178=0

a = 2; b = 14; c = -178;
Δ = b2-4ac
Δ = 142-4·2·(-178)
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-18\sqrt{5}}{2*2}=\frac{-14-18\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+18\sqrt{5}}{2*2}=\frac{-14+18\sqrt{5}}{4}
$