6k^2+5k-38=-4

Solution for 6k^2+5k-38=-4 equation:

6k^2+5k-38=-4

We move all terms to the left:

6k^2+5k-38-(-4)=0

We add all the numbers together, and all the variables

6k^2+5k-34=0

a = 6; b = 5; c = -34;
Δ = b2-4ac
Δ = 52-4·6·(-34)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*6}=\frac{-34}{12}
=-2+5/6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*6}=\frac{24}{12}
=2
$