-6/5k-5/8=-1+4/3k

Solution for -6/5k-5/8=-1+4/3k equation:

-6/5k-5/8=-1+4/3k

We move all terms to the left:

-6/5k-5/8-(-1+4/3k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 3k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-6/5k-(4/3k-1)-5/8=0

We get rid of parentheses

-6/5k-4/3k+1-5/8=0

We calculate fractions


(-225k^2)/960k^2+(-1152k)/960k^2+(-1280k)/960k^2+1=0

We multiply all the terms by the denominator


(-225k^2)+(-1152k)+(-1280k)+1*960k^2=0

Wy multiply elements

(-225k^2)+960k^2+(-1152k)+(-1280k)=0

We get rid of parentheses

-225k^2+960k^2-1152k-1280k=0

We add all the numbers together, and all the variables

735k^2-2432k=0

a = 735; b = -2432; c = 0;
Δ = b2-4ac
Δ = -24322-4·735·0
Δ = 5914624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5914624}=2432$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2432)-2432}{2*735}=\frac{0}{1470}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2432)+2432}{2*735}=\frac{4864}{1470}
=3+227/735
$