3m^2-138=5m

Solution for 3m^2-138=5m equation:

3m^2-138=5m

We move all terms to the left:

3m^2-138-(5m)=0

a = 3; b = -5; c = -138;
Δ = b2-4ac
Δ = -52-4·3·(-138)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-41}{2*3}=\frac{-36}{6}
=-6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+41}{2*3}=\frac{46}{6}
=7+2/3
$