5w^2-12w-1=-5

Solution for 5w^2-12w-1=-5 equation:

5w^2-12w-1=-5

We move all terms to the left:

5w^2-12w-1-(-5)=0

We add all the numbers together, and all the variables

5w^2-12w+4=0

a = 5; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·5·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8}{2*5}=\frac{4}{10}
=2/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8}{2*5}=\frac{20}{10}
=2
$