-4/3k-3/2k=-85/12

Solution for -4/3k-3/2k=-85/12 equation:

-4/3k-3/2k=-85/12

We move all terms to the left:

-4/3k-3/2k-(-85/12)=0


Domain of the equation: 3k!=0

k!=0/3

k!=0

k∈R



Domain of the equation: 2k!=0

k!=0/2

k!=0

k∈R


We get rid of parentheses

-4/3k-3/2k+85/12=0

We calculate fractions


1020k^2/72k^2+(-96k)/72k^2+(-108k)/72k^2=0

We multiply all the terms by the denominator


1020k^2+(-96k)+(-108k)=0

We get rid of parentheses

1020k^2-96k-108k=0

We add all the numbers together, and all the variables

1020k^2-204k=0

a = 1020; b = -204; c = 0;
Δ = b2-4ac
Δ = -2042-4·1020·0
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-204)-204}{2*1020}=\frac{0}{2040}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-204)+204}{2*1020}=\frac{408}{2040}
=1/5
$