9x^2+28x+6=0

Solution for 9x^2+28x+6=0 equation:

9x^2+28x+6=0

a = 9; b = 28; c = +6;
Δ = b2-4ac
Δ = 282-4·9·6
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{142}}{2*9}=\frac{-28-2\sqrt{142}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{142}}{2*9}=\frac{-28+2\sqrt{142}}{18}
$