2m^2-12m-19=6

Solution for 2m^2-12m-19=6 equation:

2m^2-12m-19=6

We move all terms to the left:

2m^2-12m-19-(6)=0

We add all the numbers together, and all the variables

2m^2-12m-25=0

a = 2; b = -12; c = -25;
Δ = b2-4ac
Δ = -122-4·2·(-25)
Δ = 344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{86}}{2*2}=\frac{12-2\sqrt{86}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{86}}{2*2}=\frac{12+2\sqrt{86}}{4}
$