10^2-4(m)(6m-5)=0

Solution for 10^2-4(m)(6m-5)=0 equation:

10^2-4(m)(6m-5)=0

We add all the numbers together, and all the variables

-4m(6m-5)+100=0

We multiply parentheses

-24m^2+20m+100=0

a = -24; b = 20; c = +100;
Δ = b2-4ac
Δ = 202-4·(-24)·100
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-100}{2*-24}=\frac{-120}{-48}
=2+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+100}{2*-24}=\frac{80}{-48}
=-1+2/3
$