23m=6m^2+21

Solution for 23m=6m^2+21 equation:

23m=6m^2+21

We move all terms to the left:

23m-(6m^2+21)=0

We get rid of parentheses

-6m^2+23m-21=0

a = -6; b = 23; c = -21;
Δ = b2-4ac
Δ = 232-4·(-6)·(-21)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5}{2*-6}=\frac{-28}{-12}
=2+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5}{2*-6}=\frac{-18}{-12}
=1+1/2
$