0=5k^2+12k+7

Solution for 0=5k^2+12k+7 equation:

0=5k^2+12k+7

We move all terms to the left:

0-(5k^2+12k+7)=0

We add all the numbers together, and all the variables

-(5k^2+12k+7)=0

We get rid of parentheses

-5k^2-12k-7=0

a = -5; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·(-5)·(-7)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*-5}=\frac{10}{-10}
=-1
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*-5}=\frac{14}{-10}
=-1+2/5
$