17x^2+6x+2=180

Solution for 17x^2+6x+2=180 equation:

17x^2+6x+2=180

We move all terms to the left:

17x^2+6x+2-(180)=0

We add all the numbers together, and all the variables

17x^2+6x-178=0

a = 17; b = 6; c = -178;
Δ = b2-4ac
Δ = 62-4·17·(-178)
Δ = 12140
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:

$\sqrt{\Delta}=\sqrt{12140}=\sqrt{4*3035}=\sqrt{4}*\sqrt{3035}=2\sqrt{3035}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3035}}{2*17}=\frac{-6-2\sqrt{3035}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3035}}{2*17}=\frac{-6+2\sqrt{3035}}{34}
$