7x^2+35x+14=0

Solution for 7x^2+35x+14=0 equation:

7x^2+35x+14=0

a = 7; b = 35; c = +14;
Δ = b2-4ac
Δ = 352-4·7·14
Δ = 833
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:

$\sqrt{\Delta}=\sqrt{833}=\sqrt{49*17}=\sqrt{49}*\sqrt{17}=7\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-7\sqrt{17}}{2*7}=\frac{-35-7\sqrt{17}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+7\sqrt{17}}{2*7}=\frac{-35+7\sqrt{17}}{14}
$