5m2+12m-13=-5

Solution for 5m2+12m-13=-5 equation:

5m^2+12m-13=-5

We move all terms to the left:

5m^2+12m-13-(-5)=0

We add all the numbers together, and all the variables

5m^2+12m-8=0

a = 5; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·5·(-8)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{19}}{2*5}=\frac{-12-4\sqrt{19}}{10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{19}}{2*5}=\frac{-12+4\sqrt{19}}{10}
$