3m^2-5m=4

Solution for 3m^2-5m=4 equation:

3m^2-5m=4

We move all terms to the left:

3m^2-5m-(4)=0

a = 3; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·3·(-4)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{73}}{2*3}=\frac{5-\sqrt{73}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*3}=\frac{5+\sqrt{73}}{6}
$