19m=4-m^2

Solution for 19m=4-m^2 equation:

19m=4-m^2

We move all terms to the left:

19m-(4-m^2)=0

We get rid of parentheses

m^2+19m-4=0

a = 1; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·1·(-4)
Δ = 377
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{-(19)-\sqrt{377}}{2*1}=\frac{-19-\sqrt{377}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{377}}{2*1}=\frac{-19+\sqrt{377}}{2}
$