9x^2-28x+14=0

Solution for 9x^2-28x+14=0 equation:

9x^2-28x+14=0

a = 9; b = -28; c = +14;
Δ = b2-4ac
Δ = -282-4·9·14
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{70}}{2*9}=\frac{28-2\sqrt{70}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{70}}{2*9}=\frac{28+2\sqrt{70}}{18}
$