35x^2+12x+1=330

Solution for 35x^2+12x+1=330 equation:

35x^2+12x+1=330

We move all terms to the left:

35x^2+12x+1-(330)=0

We add all the numbers together, and all the variables

35x^2+12x-329=0

a = 35; b = 12; c = -329;
Δ = b2-4ac
Δ = 122-4·35·(-329)
Δ = 46204
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:

$\sqrt{\Delta}=\sqrt{46204}=\sqrt{4*11551}=\sqrt{4}*\sqrt{11551}=2\sqrt{11551}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{11551}}{2*35}=\frac{-12-2\sqrt{11551}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{11551}}{2*35}=\frac{-12+2\sqrt{11551}}{70}
$