6m2=13m-5

Solution for 6m2=13m-5 equation:

6m^2=13m-5

We move all terms to the left:

6m^2-(13m-5)=0

We get rid of parentheses

6m^2-13m+5=0

a = 6; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·6·5
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{-(-13)-7}{2*6}=\frac{6}{12}
=1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*6}=\frac{20}{12}
=1+2/3
$