2=(3k-8)11k

Solution for 2=(3k-8)11k equation:

2=(3k-8)11k

We move all terms to the left:

2-((3k-8)11k)=0


We calculate terms in parentheses: -((3k-8)11k), so:

(3k-8)11k

We multiply parentheses

33k^2-88k

Back to the equation:

-(33k^2-88k)


We get rid of parentheses

-33k^2+88k+2=0

a = -33; b = 88; c = +2;
Δ = b2-4ac
Δ = 882-4·(-33)·2
Δ = 8008
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:

$\sqrt{\Delta}=\sqrt{8008}=\sqrt{4*2002}=\sqrt{4}*\sqrt{2002}=2\sqrt{2002}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(88)-2\sqrt{2002}}{2*-33}=\frac{-88-2\sqrt{2002}}{-66}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(88)+2\sqrt{2002}}{2*-33}=\frac{-88+2\sqrt{2002}}{-66}
$