6m^2-5m=1

Solution for 6m^2-5m=1 equation:

6m^2-5m=1

We move all terms to the left:

6m^2-5m-(1)=0

a = 6; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·6·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*6}=\frac{-2}{12}
=-1/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*6}=\frac{12}{12}
=1
$