3m^2-28m+13=0

Solution for 3m^2-28m+13=0 equation:

3m^2-28m+13=0

a = 3; b = -28; c = +13;
Δ = b2-4ac
Δ = -282-4·3·13
Δ = 628
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{157}}{2*3}=\frac{28-2\sqrt{157}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{157}}{2*3}=\frac{28+2\sqrt{157}}{6}
$