-6/5k-1/4=3+7/6k

Solution for -6/5k-1/4=3+7/6k equation:

-6/5k-1/4=3+7/6k

We move all terms to the left:

-6/5k-1/4-(3+7/6k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 6k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-6/5k-(7/6k+3)-1/4=0

We get rid of parentheses

-6/5k-7/6k-3-1/4=0

We calculate fractions


(-180k^2)/480k^2+(-576k)/480k^2+(-560k)/480k^2-3=0

We multiply all the terms by the denominator


(-180k^2)+(-576k)+(-560k)-3*480k^2=0

Wy multiply elements

(-180k^2)-1440k^2+(-576k)+(-560k)=0

We get rid of parentheses

-180k^2-1440k^2-576k-560k=0

We add all the numbers together, and all the variables

-1620k^2-1136k=0

a = -1620; b = -1136; c = 0;
Δ = b2-4ac
Δ = -11362-4·(-1620)·0
Δ = 1290496
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1290496}=1136$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1136)-1136}{2*-1620}=\frac{0}{-3240}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1136)+1136}{2*-1620}=\frac{2272}{-3240}
=-284/405
$