8k(k+4)=6k-15

Solution for 8k(k+4)=6k-15 equation:

8k(k+4)=6k-15

We move all terms to the left:

8k(k+4)-(6k-15)=0

We multiply parentheses

8k^2+32k-(6k-15)=0

We get rid of parentheses

8k^2+32k-6k+15=0

We add all the numbers together, and all the variables

8k^2+26k+15=0

a = 8; b = 26; c = +15;
Δ = b2-4ac
Δ = 262-4·8·15
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-14}{2*8}=\frac{-40}{16}
=-2+1/2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+14}{2*8}=\frac{-12}{16}
=-3/4
$