m^2+7m-4/51=0

Solution for m^2+7m-4/51=0 equation:

m^2+7m-4/51=0

We multiply all the terms by the denominator


m^2*51+7m*51-4=0

Wy multiply elements

51m^2+357m-4=0

a = 51; b = 357; c = -4;
Δ = b2-4ac
Δ = 3572-4·51·(-4)
Δ = 128265
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{-(357)-\sqrt{128265}}{2*51}=\frac{-357-\sqrt{128265}}{102}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(357)+\sqrt{128265}}{2*51}=\frac{-357+\sqrt{128265}}{102}
$