6x^2-28x+7=0

Solution for 6x^2-28x+7=0 equation:

6x^2-28x+7=0

a = 6; b = -28; c = +7;
Δ = b2-4ac
Δ = -282-4·6·7
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{154}}{2*6}=\frac{28-2\sqrt{154}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{154}}{2*6}=\frac{28+2\sqrt{154}}{12}
$