6m^2-33=7m

Solution for 6m^2-33=7m equation:

6m^2-33=7m

We move all terms to the left:

6m^2-33-(7m)=0

a = 6; b = -7; c = -33;
Δ = b2-4ac
Δ = -72-4·6·(-33)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-29}{2*6}=\frac{-22}{12}
=-1+5/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+29}{2*6}=\frac{36}{12}
=3
$