5m^2-28m+12=0

Solution for 5m^2-28m+12=0 equation:

5m^2-28m+12=0

a = 5; b = -28; c = +12;
Δ = b2-4ac
Δ = -282-4·5·12
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{34}}{2*5}=\frac{28-4\sqrt{34}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{34}}{2*5}=\frac{28+4\sqrt{34}}{10}
$