-6/5k+9/2=6-3/2k

Solution for -6/5k+9/2=6-3/2k equation:

-6/5k+9/2=6-3/2k

We move all terms to the left:

-6/5k+9/2-(6-3/2k)=0


Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

-6/5k-(-3/2k+6)+9/2=0

We get rid of parentheses

-6/5k+3/2k-6+9/2=0

We calculate fractions


(-48k)/40k^2+15k/40k^2+45k/40k^2-6=0

We multiply all the terms by the denominator


(-48k)+15k+45k-6*40k^2=0

We add all the numbers together, and all the variables

60k+(-48k)-6*40k^2=0

Wy multiply elements

-240k^2+60k+(-48k)=0

We get rid of parentheses

-240k^2+60k-48k=0

We add all the numbers together, and all the variables

-240k^2+12k=0

a = -240; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-240)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-240}=\frac{-24}{-480}
=1/20
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-240}=\frac{0}{-480}
=0
$