13k+3k(k+11)=8k-7

Solution for 13k+3k(k+11)=8k-7 equation:

13k+3k(k+11)=8k-7

We move all terms to the left:

13k+3k(k+11)-(8k-7)=0

We multiply parentheses

3k^2+13k+33k-(8k-7)=0

We get rid of parentheses

3k^2+13k+33k-8k+7=0

We add all the numbers together, and all the variables

3k^2+38k+7=0

a = 3; b = 38; c = +7;
Δ = b2-4ac
Δ = 382-4·3·7
Δ = 1360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-4\sqrt{85}}{2*3}=\frac{-38-4\sqrt{85}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+4\sqrt{85}}{2*3}=\frac{-38+4\sqrt{85}}{6}
$