63m^2-32m+3=0

Solution for 63m^2-32m+3=0 equation:

63m^2-32m+3=0

a = 63; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·63·3
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{67}}{2*63}=\frac{32-2\sqrt{67}}{126}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{67}}{2*63}=\frac{32+2\sqrt{67}}{126}
$