0=4m^2-41m+10

Solution for 0=4m^2-41m+10 equation:

0=4m^2-41m+10

We move all terms to the left:

0-(4m^2-41m+10)=0

We add all the numbers together, and all the variables

-(4m^2-41m+10)=0

We get rid of parentheses

-4m^2+41m-10=0

a = -4; b = 41; c = -10;
Δ = b2-4ac
Δ = 412-4·(-4)·(-10)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-39}{2*-4}=\frac{-80}{-8}
=+10
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+39}{2*-4}=\frac{-2}{-8}
=1/4
$